Probability Lab Report
Introduction: The purpose of this lab is to apply Mendel’s laws to predict the probability of the occurrence of a single event, of two independent events and of certain traits in offspring of parents exhibiting traits. Gregor Mendel was an Austrian monk in 1866, who studied how traits were passed using pea plants. From his studies of inheritance, he created three laws of inheritance: the law of dominance, the law of segregation, and the law of independent assortment. He called genes ‘’factors’’ and believed the controlled every trait. The law of dominance states that the dominant gene prevents the appearance of the recessive gene. The law of segregation states that during gamete formation, the pair of genes separate, do that each gamete has
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only one gene for the trait. The law of independent assortment states that as gametes are being formed, the genes for various traits separate independently of one another. The creation of Mendel’s laws allows us to predict the inheritance of traits.
Materials: Two pennies, pen or pencil, and your lab.
Procedure/Method:
I. Occurrence of a Single Event
1. The law of probability states that when a procedure can result in two equally likely outcomes (in this case, heads or tails), the probability of either outcome occurring is ½, or 50%.
2. Using the law of probability, decide how many times out of 20 tosses you would expect heads to appear and how would expect tails to appear. Write your answers in the in the Expected column for 20 tosses in Table 1 of your worksheet.
3. Toss a penny 20 times. Have your partner count how many times it lands heads up and how many times it lands tails up. Write the totals under the Observed column for 20 tosses in Table I of your worksheet.
4. Calculate the deviation by subtracting the expected number from the observed number. Record these in the Deviation column for 20 tosses in Table 1 of your worksheet. Make all numbers positive (The absolute value l l of the deviation).
5. Calculate the expected numbers of heads and tails for tossing a coin and record them in the proper column in Table 1. Have your partner repeat Step 1, but tossing the penny 30 tosses in Table 1. Calculate the deviations, and enter these in the proper column.
6. Now repeat Step 1, tossing the penny 50 times. Record the observed numbers, the expected numbers, and deviations in the columns for 50 tosses in Table 1.
7. Add the observed numbers of heads and tail from the three trials and record the totals in the Total columns in Table 1. Then calculate and record the deviations.
II.
Independent Events Occurring Simultaneously
8. According to the law of probability, when there are four likely outcomes from a procedure, the probability that one of the outcomes will occur is ¼ or 25% we can see how this is calculate. For examples we know that in tossing two pennies, the probability of heads occurring on one penny is ½. The probability of head occurring on both pennies is ½ x ½ = ¼.
9. Using the law of probability, predict the expected outcomes of tossing two pennies. Record the expected outcomes in the proper column in Table 2. Calculate the percent of the total that each combination is expected to occur. To find the percent, divide each expected number by 40 and multiply 100. Enter these numbers in the proper column.
10. Toss two pennies simultaneously 40 times. Have your partner keep track of how many times heads/heads, heads/tails, tails/tails occur. Count tails/heads and heads/tails together. Record the number for each combination in the observed column in Table 2 in your worksheet.
11. Calculate the percent of the total that each combination heads/heads, heads/tails, or tails/tails) occurred and record it in the proper column in Table 2. To find the percent, divide each observed number by 40 and multiply by …show more content…
100.
12. Calculate the deviation by subtracting the expected from the observed and enter your results in Table 2.
Data: Table 1. Probability of the Occurrence of a Single Event Heads Tails
20 Tosses Expected 10 10 Observed 9 11 Deviation 1 1
30 Tosses Expected 15 15 Observed 16 14 Deviation 1 1
50 Tosses Expected 25 25 Observed 28 22 Deviation 2 3
Total Expected 50 50 Observed 55 47 Deviation 4 5 Table 2. Probability of Independent Events Occurring Simultaneously
Combinations Expected % Expected Observed % Observed Deviation
Heads-Heads 10 25% 11 30% 2 Heads-Tails or Tails-Heads 20 50% 13 45% 2 Tails-Tails 10 25% 10 25% 0 Total 40 100 40 100 4
Post-Lab Questions:
1.
In Part 1, what was the expected ratio of heads to tails for tosses of a single coin? 1:1. Did your results always agree with the expected ratio? If not, what would be a reason for the deviation?
My results did not always agree with the expected ratio and the reason for the deviation would be that the principles of probability made it possible to get either sides of the coin a 50:50 chance but it’s not probable.
2. Compare the deviations from the expected for 20, 30, and 50 tosses. What seems to be the relationship between sample size and deviation? In other words, as the sample size increases, what happens to the size of the deviation?
As the sample size increased the size of the deviation decreased, but my results were very close to the expected numbers.
3. In part 2, what was the probability that tails would appear on both coins? 25%. How did you arrive at this answer?
HH Ht tt H I arrived at this answer by creating a punnet square which revealed that out of the four sections one was purely recessive (tails) and ¼ equals
25%. t Ht
4. Draw punnett square for an RR plant crossed an rr plant, would the offspring have round peas (R) or wrinkled peas (r)? R R The offspring would have round peas (R). Rr Rr Rr Rr r r
5. Which of Mendel’s laws did you apply to answer question 4?
I applied Mendel’s law of dominance.
6. Draw a Punnett square to illustrate the cross of Rr and Rr plants. What is the probability that the plants will have round peas? 75%
R r RR Rr Rr rr R r Conclusion: From doing this lab, I have learnt some of the principles of probability. I have also learned what the three laws of inheritance are, how to apply them to certain questions, and that they were created by Gregor Mendel. I learned how to use punnett squares properly and how to decide the percentage of the inheritance of traits using it. The information gained in this lab would be useful in Forensics, if I got a job in the medical field and for later on in Living Environment. Any sources of error in this lab would be messing up in counting your penny tosses, which would lead to the whole first table being wrong.
only one gene for the trait. The law of independent assortment states that as gametes are being formed, the genes for various traits separate independently of one another. The creation of Mendel’s laws allows us to predict the inheritance of traits.
Materials: Two pennies, pen or pencil, and your lab.
Procedure/Method:
I. Occurrence of a Single Event
1. The law of probability states that when a procedure can result in two equally likely outcomes (in this case, heads or tails), the probability of either outcome occurring is ½, or 50%.
2. Using the law of probability, decide how many times out of 20 tosses you would expect heads to appear and how would expect tails to appear. Write your answers in the in the Expected column for 20 tosses in Table 1 of your worksheet.
3. Toss a penny 20 times. Have your partner count how many times it lands heads up and how many times it lands tails up. Write the totals under the Observed column for 20 tosses in Table I of your worksheet.
4. Calculate the deviation by subtracting the expected number from the observed number. Record these in the Deviation column for 20 tosses in Table 1 of your worksheet. Make all numbers positive (The absolute value l l of the deviation).
5. Calculate the expected numbers of heads and tails for tossing a coin and record them in the proper column in Table 1. Have your partner repeat Step 1, but tossing the penny 30 tosses in Table 1. Calculate the deviations, and enter these in the proper column.
6. Now repeat Step 1, tossing the penny 50 times. Record the observed numbers, the expected numbers, and deviations in the columns for 50 tosses in Table 1.
7. Add the observed numbers of heads and tail from the three trials and record the totals in the Total columns in Table 1. Then calculate and record the deviations.
II.
Independent Events Occurring Simultaneously
8. According to the law of probability, when there are four likely outcomes from a procedure, the probability that one of the outcomes will occur is ¼ or 25% we can see how this is calculate. For examples we know that in tossing two pennies, the probability of heads occurring on one penny is ½. The probability of head occurring on both pennies is ½ x ½ = ¼.
9. Using the law of probability, predict the expected outcomes of tossing two pennies. Record the expected outcomes in the proper column in Table 2. Calculate the percent of the total that each combination is expected to occur. To find the percent, divide each expected number by 40 and multiply 100. Enter these numbers in the proper column.
10. Toss two pennies simultaneously 40 times. Have your partner keep track of how many times heads/heads, heads/tails, tails/tails occur. Count tails/heads and heads/tails together. Record the number for each combination in the observed column in Table 2 in your worksheet.
11. Calculate the percent of the total that each combination heads/heads, heads/tails, or tails/tails) occurred and record it in the proper column in Table 2. To find the percent, divide each observed number by 40 and multiply by …show more content…
100.
12. Calculate the deviation by subtracting the expected from the observed and enter your results in Table 2.
Data: Table 1. Probability of the Occurrence of a Single Event Heads Tails
20 Tosses Expected 10 10 Observed 9 11 Deviation 1 1
30 Tosses Expected 15 15 Observed 16 14 Deviation 1 1
50 Tosses Expected 25 25 Observed 28 22 Deviation 2 3
Total Expected 50 50 Observed 55 47 Deviation 4 5 Table 2. Probability of Independent Events Occurring Simultaneously
Combinations Expected % Expected Observed % Observed Deviation
Heads-Heads 10 25% 11 30% 2 Heads-Tails or Tails-Heads 20 50% 13 45% 2 Tails-Tails 10 25% 10 25% 0 Total 40 100 40 100 4
Post-Lab Questions:
1.
In Part 1, what was the expected ratio of heads to tails for tosses of a single coin? 1:1. Did your results always agree with the expected ratio? If not, what would be a reason for the deviation?
My results did not always agree with the expected ratio and the reason for the deviation would be that the principles of probability made it possible to get either sides of the coin a 50:50 chance but it’s not probable.
2. Compare the deviations from the expected for 20, 30, and 50 tosses. What seems to be the relationship between sample size and deviation? In other words, as the sample size increases, what happens to the size of the deviation?
As the sample size increased the size of the deviation decreased, but my results were very close to the expected numbers.
3. In part 2, what was the probability that tails would appear on both coins? 25%. How did you arrive at this answer?
HH Ht tt H I arrived at this answer by creating a punnet square which revealed that out of the four sections one was purely recessive (tails) and ¼ equals
25%. t Ht
4. Draw punnett square for an RR plant crossed an rr plant, would the offspring have round peas (R) or wrinkled peas (r)? R R The offspring would have round peas (R). Rr Rr Rr Rr r r
5. Which of Mendel’s laws did you apply to answer question 4?
I applied Mendel’s law of dominance.
6. Draw a Punnett square to illustrate the cross of Rr and Rr plants. What is the probability that the plants will have round peas? 75%
R r RR Rr Rr rr R r Conclusion: From doing this lab, I have learnt some of the principles of probability. I have also learned what the three laws of inheritance are, how to apply them to certain questions, and that they were created by Gregor Mendel. I learned how to use punnett squares properly and how to decide the percentage of the inheritance of traits using it. The information gained in this lab would be useful in Forensics, if I got a job in the medical field and for later on in Living Environment. Any sources of error in this lab would be messing up in counting your penny tosses, which would lead to the whole first table being wrong.