Probability Exercise

1. A gambler in Las Vegas is cutting a deck of cards for $1,000. What is the probability that the card for the gambler will be the following? a. A face card – there are 12 face cards in a deck of 52 cards. The probability would be 12/52 b. A queen – there are 4 queens in a deck, so the probability would be 4/52 c. A Spade - There are 13 cards of each suit so the probability is 13/52 or ¼. d. A jack of spades - There is only 1 jack of spades in a deck, so the probability would be 1/52
2. The employees in the textile industry can be segmented as follows:
Employees
number
Probability
Female and union 12,000
0.12
Female and nonunion 25,000
0.25
Male and union 21,000
0.21
Male and nonunion 42,000
0.42
Total 100,000
1
a. Determine the probability of each even in this distribution. Probability of female and union is 12000/100000= .12 Probability of female and nonunion is 25000/100000= .25 Probability of male and union is 21000/100000= .21 Probability of male and nonunion is 42000/100000= .42
b. Are the events in this distribution mutually exclusive? Explain. Mutually exclusive means that only one of the events can occur at a time. In this case they are mutually exclusive because they can’t occur at the same.
c. What is the probability that an employee is male?
To calculate the probability that an employee is male, add up the two groups that are male: Male and union (21,000) + Male and nonunion (42,000) = 63,000
Then divide that by the total number of employees which is 80,000. 63,000 / 80,000 = .63

d. Is this experiment of segmenting employees in the textile industry collectively exhaustive? Explain. This experiment is collectively exhaustive because the four events in the experiment are all that occur.

3. The Jefferson High School Band Booster Club has organized a raffle. The prize is a $6,000 car. Two thousand tickets to the raffle are to be sold at $1 apiece. If a person purchase four tickets,