Problem 5. (5 points) A typical deck of cards has 4 suits V, : and the following

Question

Problem 5. (5 points) A typical deck of cards has 4 suits V, : and the following 13 denominations: Ace, 2 thru 10, Jack, Queen, and king. A full deck contains 52 cards. A single card has three 11023 characteristics: suit, denomination and colour. examples: [King of , is redj or [4 of 4, is blackj etc. (a) Say 5 cards are selected from the deck of 52, without replacement. Let X be the number of 's drawn. What is the standard deviation of X, SD[X] =? SDX =0.9295 iii (use at least four digits after the decimal point if rounding) (b) If 32 cards are selected from the deck of 52, with replacement and you are also told the number of-'s drawn is at most 12 but at least 3, what is the probability there will be exactly 7-'s draw Probability E (use at least four digits after the decimal point if rounding)

Explanation / Answer

32 cards are drawn from 52 cards

exactly 7 clubs are drawn

This means that 32-7=25 cards were from 52-13=39 cards

So we have to choose 25 cards from 39 cards with replacement

Number of ways of doing it

=39C25

Total number of ways of choosing 32 cards from 52=52C32

Probability=39C25/52C32=0.000119723=0.0001

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