Separate the 13 spades from a standard deck of cards. Three of them are picture

Question

Separate the 13 spades from a standard deck of cards. Three of them are picture cards: the Jack, Queen, and King. Now draw two cards at random from these 13 spades. Find the probability (rounded to the nearest .01%) that (a) both of the cards drawn are picture cards, if they are drawn i. without replacement. ii. with replacement. (b) at least one of the two cards drawn is a picture card, if they drawn i. without replacement. ii. with replacement. An 11-digit number is randomly chosen by drawing 11 times from a box that has one ticket for each of the numbers 0 to 9 and writing down numbers on the tickets in the order in which they are drawn. Find the chance that exactly 2 of the digits in the number chosen are sevens.

Explanation / Answer

4)

a)

Without replacement

No of ways of selecting 2 picture cards = 3C2 = 3

No of ways of selecting 2 cards from 13 card = 13C2

Probablity = 3/13C2 = 3.85% probability

b)

With replacement

No of ways of selecting 2 picture cards = 3*3 = 9

No of ways of selecting 2 out of 13 = 13*13 = 169

Probability = 9/169 = 5.33 %

b)

Probability of not a picture card = (13-3)C2/13C2 = 57.69

Probabilityof atleast one is a picture cards = 100-57.59 = 42.31%

With replacement

Probability of not a picture card = (13-3)(13-3)/13*13 = 100/169 = 59.17%

Probability of selecting atleast one picture card = 100-59.17% = 40.83%

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