Questions on Probability
6.4 Dependent and Independent Events
McGraw-Hill Ryerson Mathematics of Data Management, pp. 327–335
1. Classify each of the following pairs of events as either dependent or independent.
First Event
Second Event
a)
having blue eyes having a special musical talent
b)
graduating high school gaining entrance into college
c)
giving birth to a male child giving birth to a second male child
d)
passing a police cruiser while speeding obtaining a speeding ticket
e)
drawing an ace from a standard deck of cards drawing a second ace from a standard deck of cards, without replacing the first
f)
drawing an ace from a standard deck of cards drawing a second ace from a standard deck of cards, after replacing the first
2. What is the probability of drawing each of the following from a standard deck of cards, assuming that the first card is not replaced?
a) an ace followed by a 2 b) two aces
c) a black jack followed by a 3 d) a face card followed by a black 7
3. Repeat each part of question 2, assuming that the first card drawn is replaced and the deck shuffled prior to selecting the second card.
4. What are the odds in favour of rolling a 7, or an 11, or doubles twice in a row with a pair of standard dice?
5. Paulo’s marker is seven squares away from “home”. He must land exactly on home to win the game. If he rolls a standard die and moves his marker the number of squares indicated, what is the probability that Paulo will win the game
a) on his next turn? b) on his next two turns?
6. Eight burglary suspects are placed in a line-up, two of whom are guilty. Suppose that a witness is asked to identify the two guilty suspects, but is actually unable to make a positive identification with any degree of confidence. If the witness feels compelled to identify two suspects, what is the likelihood that the witness will randomly pick
a) the two guilty suspects? b) two innocent suspects?
7. A quality control inspector will accept a large
McGraw-Hill Ryerson Mathematics of Data Management, pp. 327–335
1. Classify each of the following pairs of events as either dependent or independent.
First Event
Second Event
a)
having blue eyes having a special musical talent
b)
graduating high school gaining entrance into college
c)
giving birth to a male child giving birth to a second male child
d)
passing a police cruiser while speeding obtaining a speeding ticket
e)
drawing an ace from a standard deck of cards drawing a second ace from a standard deck of cards, without replacing the first
f)
drawing an ace from a standard deck of cards drawing a second ace from a standard deck of cards, after replacing the first
2. What is the probability of drawing each of the following from a standard deck of cards, assuming that the first card is not replaced?
a) an ace followed by a 2 b) two aces
c) a black jack followed by a 3 d) a face card followed by a black 7
3. Repeat each part of question 2, assuming that the first card drawn is replaced and the deck shuffled prior to selecting the second card.
4. What are the odds in favour of rolling a 7, or an 11, or doubles twice in a row with a pair of standard dice?
5. Paulo’s marker is seven squares away from “home”. He must land exactly on home to win the game. If he rolls a standard die and moves his marker the number of squares indicated, what is the probability that Paulo will win the game
a) on his next turn? b) on his next two turns?
6. Eight burglary suspects are placed in a line-up, two of whom are guilty. Suppose that a witness is asked to identify the two guilty suspects, but is actually unable to make a positive identification with any degree of confidence. If the witness feels compelled to identify two suspects, what is the likelihood that the witness will randomly pick
a) the two guilty suspects? b) two innocent suspects?
7. A quality control inspector will accept a large