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# Probability scenarios

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Looking for assistance to make sure I am calculation answers correctly for the following 2 scenarios.

Please provide the answer and any formulas in excel spreadsheet.

A standard deck of playing cards consists of fifty-two cards. The cards in each deck consist of four suits, namely spades (♠), clubs (♣), diamonds (♦) and hearts (♥). Each suit consists of thirteen cards, namely ace, king, queen, jack, 10, 9, 8, 7, 6, 5, 4, 3, and 2. In the game of poker, a royal flush consists of the ace, king, queen, jack, and 10 of the same suit (e.g., ace of spades, king of spades, queen of spades, jack of spades and 10 of spades).

1. What is the probability of randomly selecting five cards from a randomly shuffled deck of playing cards that constitute a royal flush, assuming the order in which the cards are selected is irrelevant (i.e., not important) and the suit is irrelevant (i.e., not important)?
a.1.5 x 10-6
b.3.6 x 10-7
c.7.1 x 10-8
d.1.5 x 10-8

2. What is the probability of randomly selecting five cards from a randomly shuffled deck of playing cards that constitute a royal flush, assuming the cards must be selected in a specific order, namely ace, king, queen, jack and 10, and the suit is irrelevant (i.e., not important)?
a.1.3 x 10-6
b.2.6 x 10-6
c.1.3 x 10-8
d.7.1 x 10-8

Next Scenario:

50 students in two sections of a college Physics 101 course recently took a mid-term exam. 13 students earned an A, 10 students earned a B, 8 students earned a C, 9 students earned a D and 10 students earned an F on the exam. The students were queried regarding the number of hours they had devoted to studying for the exam. 12 of the students who earned an A, 8 of the students who earned a B, 6 of the students who earned a C, 2 of the students who earned a D, and 1 of the students who earned an F reported that they had devoted more than 8 hours to studying for the exam. The remaining students reported that they had devoted no more than 8 hours to studying for the exam.

1.What is the probability of a randomly selected student having earned an A on the exam?
a.0.15
b.0.26
c.0.32
d.0.07

2. What is the probability of a randomly selected student having earned an F on the exam?
a.0.20
b.0.27
c.0.36
d.0.17

3.What is the probability of a randomly selected student having devoted no more than 8 hours to studying for the exam?
a.0.51
b.0.34
c.0.42
d.0.29

4.What is the probability of a randomly selected student having earned an A on the exam given they devoted no more than 8 hours to studying for the exam?
a.0.12
b. 0.21
c.0.17
d.0.05

5.What is the probability of a randomly selected student having earned an F on the exam given they devoted more than 8 hours to studying for the exam?
a.0.12
b.0.03
c.0.09
d.0.17

6.What is the probability of a randomly selected student having earned an A or a B on the exam given they devoted more than 8 hours to studying for the exam?
a.0.57
b.0.47
c.0.69
d.0.76

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#### Solution Summary

The solution provides explanations how to find out the probability based on combination or permutation.

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## statistics - probabilities scenario participants

Read the scenario attached.

The data given:

Suppose 200 men and 200 women participate in a study and 280 report they prefer plain water. Of the participants preferring a sports drink, 80 were men and 40 were women.

Find the various probabilities under a - f (omit g) below.

a. What is the probability that a person prefers water?
b. What is the probability that a person prefers the sports drinks?
c. Probability of being male given they prefer a sports drink:
Probability of being a female given they prefer a sports drink:
d. Probability of both male and preferring sports drink:
Probability of both female and preferring sports drink:
e. Given that the consumer is a man, what is the probability he prefers sports drinks?
f. Given that the consumer is a woman, what is the probability she prefers sports drinks?

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