Concept explainers
Selecting a Card When a card is drawn from a deck, find the probability of getting
a. A diamond
b. A 5 or a heart
c. A 5 and a heart
d. A king
e. A red card
a.
To obtain: The probability of getting a diamond.
Answer to Problem 24CQ
The probability of getting a diamond is
Explanation of Solution
Calculation:
In ordinary deck of cards there are 4 suits. They are hearts, clubs, diamonds and spades. In each suite there are 13 cards. In 13 cards, nine cards are numbers from 2 to 10 and remaining four cards are king, queen, ace and jack cards.
The total number of outcomes is 52.
Let event A denote getting a diamond.
The possible number of outcomes for getting diamonds is 13.
That is, there are 13 outcomes for getting an event A.
The formula for probability of event A is,
Substitute 13 for ‘Number of outcomes in A’ and 52 for ‘Total number of outcomes in the sample space’,
Thus, the probability of getting a diamond is
b.
To obtain: The probability of getting a 5 or a heart.
Answer to Problem 24CQ
The probability of getting a 5 or a heart is
Explanation of Solution
Calculation:
Let event B denote getting a 5.
The possible number of outcomes for getting a 5 is 5.
That is, there are 4 outcomes for getting an event B.
The formula for probability of event B is,
Substitute 4 for ‘Number of outcomes in B’ and 52 for ‘Total number of outcomes in the sample space’,
Let event C denote getting a heart.
The possible number of outcomes for getting a heart is 13.
That is, there are 13 outcomes for getting an event C.
The formula for probability of event C is,
Substitute 13 for ‘Number of outcomes in C’ and 52 for ‘Total number of outcomes in the sample space’,
The formula for probability of event A and B is,
Substitute 1 for ‘Number of outcomes in B and C’ and 52 for ‘Total number of outcomes in the sample space’,
Addition Rule:
The formula for probability of getting event B or event C is,
Substitute
Thus, the probability of getting a 5 or a heart is
c.
To obtain: The probability of getting a 5 and a heart.
Answer to Problem 24CQ
The probability of getting a 5 and a heart is
Explanation of Solution
Calculation:
Let event D denote getting a 5 and a heart.
The possible number of outcomes for getting a 5 and a heart is 1.
That is, there are 1 outcomes for getting an event D.
The formula for probability of event D is,
Substitute 1 for ‘Number of outcomes in D’ and 52 for ‘Total number of outcomes in the sample space’,
d.
To obtain: The probability of getting a king.
Answer to Problem 24CQ
The probability of getting a king is
Explanation of Solution
Calculation:
Let event E denote getting a king.
The possible number of outcomes for getting a king is 4.
That is, there are 4 outcomes for getting an event E.
The formula for probability of event E is,
Substitute 4 for ‘Number of outcomes in E’ and 52 for ‘Total number of outcomes in the sample space’,
Thus, probability of getting a king is
e.
To obtain: The probability of getting a red card.
Answer to Problem 24CQ
The probability of getting a red card is
Explanation of Solution
Calculation:
Let event F denote getting a red card.
The possible number of outcomes for getting a red card is 26.
That is, there are 26 outcomes for getting an event F.
The formula for probability of event F is,
Substitute 26 for ‘Number of outcomes in E’ and 52 for ‘Total number of outcomes in the sample space’,
Thus, probability of getting a red card is
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Chapter 4 Solutions
Elementary Statistics: A Step By Step Approach
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