Four cards are dealt from a deck of 52 cards What is the pro

Four cards are dealt from a deck of 52 cards. What is the probability that the ace of spades is one of the 4 cards? Suppose one of the 4 cards is chosen at random and found not to be the ace of spades. What is the probability that none of the 4 cards is the ace of spades? Suppose the experiment in part (b) is repeated a total of 10 times (replacing the card looked at each time), and the ace of spades is not seen. What is the probability that the ace of spades actually is one of the 4 cards? The probability that the ace of spades is one of the 4 cards is

Solution

a) 10 cards are taken from 52 cards

Total no. of possobilities of selecting 10 cards = ⁵²c₁₀

0f 10 cards, 1 card is ace spade, possibilities = ⁵¹c₉

Therefore, probability that one card is ace of spade =  (⁵¹c₉ )/ (⁵²c₁₀ ) = 5/26

b) probability that no card is ace of spade =  (⁵²c₁₀ - ⁵¹c₉ )/ (⁵²c₁₀ ) = 21/26