2drdshas been reducedtoStea standard deck of 52 cards consists oftg13 clubs (113

Question

2drdshas been reducedtoStea standard deck of 52 cards consists oftg13 clubs (113 spades (),13 hearts) and 13 diamonds() 6. Astandarddeck cause a nknown card was lost. As are minder a a. A card is selected at random from the 51 cards, and we observe that this card is a diamond. Given this information, find the probability that the lost card is a cluby (Answer:0.2549) b. Four cards are selected at random without replacement from the 51 cards, and we observe that all are hearts. Given this information, find the probability that the lost card is a club. (Answer: 0.2708)

Explanation / Answer

a. Since the selected card is a diamond, the rest of the 51 cards (including the lost card) comprise of 13 each of spades, clubs and hearts and 12 diamonds.

Probability that the lost card is a club = 13/51 = 0.2549.

b. Since the four selected cards are all hearts, the rest of the 48 cards (including the lost card) comprise of 13 each of spades, clubs and diamonds and 9 hearts.

Probability that the lost card is a club = 13/48 = 0.2708.

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