Concept explainers
Drawing a Card Four cards are drawn from a desk without replacement. Find these probabilities.
a. All cards are jacks.
b. All cards are black cards.
c. All cards are hearts.
a.
To find: The probability that all 4 cards are jacks.
Answer to Problem 13E
The probability that all 4 cards are jacks is
Explanation of Solution
Given info:
The number of jacks in a desk is 4.
Calculation:
Here, the selections are made without replacement. Thus, the selections are dependent.
Multiplication rule for dependent events:
If the events A and B are dependent, the probability of occurring of event B is affected by event A, that is
Then the probability that all 4 cards are jacks is,
Thus, the probability that all 4 cards are jacks is
b.
To find: The probability that all 4 cards are black cards.
Answer to Problem 13E
The probability that all 4 cards are black cards is
Explanation of Solution
Given info:
The number of black cards in a desk is 26.
Calculation:
Here, the selections are made without replacement. Thus, the selections are dependent.
Then the probability that all 4 cards are black cards is,
Thus, the probability that all 4 cards are black cards is
c.
To find: The probability that all 4 cards are hearts.
Answer to Problem 13E
The probability that all 4 cards are hearts is
Explanation of Solution
Given info:
The number of hearts in a desk is 13.
Calculation:
Here, the selections are made without replacement. Thus, the selections are dependent.
Then the probability that all 4 cards are hearts is,
Thus, the probability that all 4 cards are hearts is
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Chapter 4 Solutions
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