You pick three cards at random from a standard deck of 52 cards. This is done tw

Question

You pick three cards at random from a standard deck of 52 cards. This is done twice, once with replacement and once without replacement. Find the probability of each event described below. Give your answers to three decimal places. 1. Your cards are all black (that is, all spades or clubs) With replacement: Without replacement: 2. You get all hearts. With replacement: Without replacement 3. You get no hearts. With replacement: Without replacement: 4. You get all picture cards With replacement: Without replacement

Explanation / Answer

Question 1

All cards are black.

(a) With replacement :

Pr(all 3 out of 3 cards are black) = (26/52) * (26/52) * (26/52) = 1/8 = 0.125

Without replacement :

Pr(all 3 out of 3 cards are black) = (26/52) * (25/51) * (24/50) = 2/17 = 0.1176

(b)

With replacement :

Pr(all 3 out of 3 cards are hearts) = (13/52) * (13/52) * (13/52) = 1/43 = 1/64

Without replacement :

Pr(all 3 out of 3 cards are hearts) = (13/52) * (12/51) * (11/50) = 0.0129

(c)

With replacement :

Pr(none is hearts) = (39/52) * (39/52) * (39/52) = (3/4)3 = 27/64

Without replacement :

Pr(none is hearts) = (39/52) * (38/51) * (37/50) = 0.4135

(d) there are 12 picture cards

With replacement :

Pr(got all picture cards) = (12/52) * (12/52) * (12/52) = (3/13)3 = 27/2197

Without replacement :

Pr(got all picture cards) = (12/52) * (11/51) * (10/50) = 0.0099 or 0.01

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