(a)
Obtain the chance of getting only kings in a deck.
(a)
Answer to Problem 15SRE
The chance of getting only kings in a deck is 0.000181.
Explanation of Solution
Calculation:
In general, a standard deck of cards contains 52 cards, of which 26 are red and 26 are black, 13 are of each suit (hearts, diamonds, spades, and clubs) and of which 4 are of each denomination (A, 2 to 10, J, Q, and K). There are 4 face cards. That is, jacks J, queen Q, and kings K.
The
Here, 4 of 52 cards in the standard deck of cards are kings.
The probability is given below:
Once a king has been selected, 3 of 51 cards in the standard deck of cards are kings.
The probability is given below:
Once two kings have been selected, 2 of 50 cards in the standard deck of cards are kings.
The probability is given below:
General multiplication rule:
Therefore, the chance of getting only kings in a deck is given below:
(b)
Obtain the chance of getting no kings in a deck.
(b)
Answer to Problem 15SRE
The chance of getting no kings in a deck is 0.7826.
Explanation of Solution
Calculation:
Here, 48 of 52 cards in the standard deck of cards are not kings.
The probability is given below:
Once a non-king has been selected, 47 of 51 cards in the standard deck of cards are not kings.
The probability is given below:
Once two non-kings have been selected, 46 of 50 cards in the standard deck of cards are not kings.
The probability is given below:
Therefore, the chance of getting no kings in a deck is given below:
(c)
Obtain the chance of getting no face cards.
(c)
Answer to Problem 15SRE
The chance of getting no face cards in a deck is 0.4471.
Explanation of Solution
Calculation:
Here, 40 of 52 cards in the standard deck of cards are not face cards.
The probability is given below:
Once a non-face card has been selected, 39 of 51 cards in the standard deck of cards are not face cards.
The probability is given below:
Once two non-face cards have been selected, 38 of 50 cards in the standard deck of cards are not face cards.
The probability is given below:
Therefore, the chance of getting no face cards in a deck is given below:
(d)
Obtain the chance of getting at least one face card.
(d)
Answer to Problem 15SRE
The chance of getting at least one face card in a deck is 0.5529.
Explanation of Solution
Calculation:
From Part (d), the chance of getting no face cards in a deck is 0.4471.
Therefore, the chance of getting at least one face card in a deck is given below:
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Chapter 29 Solutions
Statistics
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