Question
Asked Mar 20, 2019
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10. Selecting Cards The red face cards and the black car
ds
numbered 2-9 are put into a bag. Four cards are drawn
at random without replacement. Find the following
probabilities.
a. All 4 cards are red.
b. 2 cards are red and 2 cards are black.
c. At least 1 of the cards is red
d. All 4 cards are black.
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10. Selecting Cards The red face cards and the black car ds numbered 2-9 are put into a bag. Four cards are drawn at random without replacement. Find the following probabilities. a. All 4 cards are red. b. 2 cards are red and 2 cards are black. c. At least 1 of the cards is red d. All 4 cards are black.

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Expert Answer

Step 1

Part (a):

A standard deck of cards contains 52 cards. Out of these, there are 26 red cards and 24 black cards.

Also, a suit of 52 cards is divided into 4 suits, 2 suits of red cards and 2 of black cards.

Each suit contains 13 cards- 3 face cards (King, Queen and Jack), 9 numbered cards (2 to 10) and one Ace.

As there are 2 suits of red cards, total number of red face cards in the bag is 3 + 3 = 6.

As there are 2 suits of black cards, total number of black cards numbered 2 to 9 in the bag is 8 + 8 = 16.

Total number of cards in the bag is 6 + 16 = 22.

Four cards are randomly drawn from the bag. The total number of ways in which 4 cards can be randomly selected from 22 cards is 22 combinations 4.

If all four cards are red, it means that 4 cards are selected from the 6 red cards and none is selected from the 16 black cards.

The probability that all four cards drawn are red is:

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Step 2

Part (b):

If two cards are red and two are black, it means that 2 cards are selected from the 6 red cards and 2 are selected from the 16 black cards.

The probability that two of the four cards drawn are red and two are black is:

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Step 3

Part (c):

The probability that at least one of the cards drawn is red is the probabi...

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