Ten cords are dealt from a deck of 52 cards (a) What is the probability that the

Question

Ten cords are dealt from a deck of 52 cards (a) What is the probability that the ace of spades is one of the 10 cards? (b) Suppose one of the 10 cards is chosen at random and found not to be the ace of spades. What is the probability that none of the 10 cards is the ace of spades? (c) 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 10 cards? (a) The probability that the ace of spades is one of the 10 cards is .(Simplify your answer. Round to three decimal places as needed.)

Explanation / Answer

For a) we can used two methods

1) We draw sample of sized 10 from a deck of 52 cards.

There are only one Ace of Spades

So probability of it include in the sample of size 10 is 10/52 = 0.192

2) using combination method

We want to select 1 spade of Ace from 1 so total ways = 1

We select othere 9 cards from 51 remaining cards = 51C9 ways = 3042312350 ways

So possible ways = 1*3042312350 = 3042312350

Total ways = 52C9 ways = 15820024220

Probability = possible ways / total wyas =3042312350 / 15820024220 = 0.192

b) We want to find probability ofnot spades card in the sample of size 10

That is complement o

f first part

therefore required probability = 1 - 0.192 = 0.808

c) In this part we want to find probability of ace of spade is one of the 10 times

By using Binomial distribution we need to find probability for x = 1, p = 0.1923 and n =10

Using binomial command as "=BINOMDIST(1,10,0.1923,0)" and then enter we get

required probability = 0.281

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