10. Five cards are drawn from a well shuffled pack of 52 playing cards. It can be shown that
(disregarding the order in which the cards are dealt) there are 2,598,960 possible fivecard
hands, of which only 1287 are hands consisting entirely of spades. What is the
probability that a hand will consist entirely of spades?
(a) 0.004956
(b) 0.003560
(c) 0.000495
(d) 0.006578
(e) 0.000295
11. From a group consisting of 20 married couples, one man and one woman are selected.
Suppose that all selections are equally likely. What is the probability that the selected
man and woman are married to each other?
(a) 1 /2
(b) 1/10
(c) 1/20
(d) 2/20
10. Divide spades by total possible.
11. If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
P(M) = 1/20 * 1/10 (once first person chosen, second must be opposite gender, unless you are considering Supreme Court decision.)
Do you have a typo?
To find the probability of a certain event, we need to divide the number of favorable outcomes by the total number of possible outcomes.
For question 10:
The total number of possible five-card hands is given as 2,598,960.
The number of hands consisting entirely of spades is given as 1287.
Therefore, the probability of a hand consisting entirely of spades is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 1287 / 2,598,960
Simplifying the fraction, we get:
Probability = 0.000495
So the answer is (c) 0.000495.
For question 11:
We have a group consisting of 20 married couples, so there are 40 people in total.
The number of ways to select one man is 20, and the number of ways to select one woman is also 20.
Since each selection is equally likely, the total number of possible selections is 20 * 20 = 400.
Out of these 400 selections, there are 20 where the selected man and woman are married to each other (each man is married to one woman, so there are 20 such pairs).
Therefore, the probability that the selected man and woman are married to each other is:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 20 / 400
Simplifying the fraction, we get:
Probability = 1/20
So the answer is (c) 1/20.