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5 cards are drawn successively from a well-shuffled pack of 52 cards with replacement. Determine the probability that (i) all the five cards should be spades? (ii) only 3 cards should be spades? (iii) none of the cards is a spade?
5 cards are drawn successively from a well-shuffled pack of 52 cards with replacement. Determine the probability that (i) all the five cards should be spades? (ii) only 3 cards should be spades? (iii) none of the cards is a spade?

```
3 months ago Anand Kumar Pandey
3069 Points
```							Dear StudentLet us assume that X be the number of spade cardsUsing the Bernoulli trial, X has a binomial distributionP(X = x) =nCxq^(n-x) p^xThus, the number of cards drawn, n = 5Probability of getting spade card, p = 13/52 = 1/4Thus the value of the q can be found usingq = 1 – p = 1 – (1/4)= 3/4Now substitute the p and q values in the formula,Hence, P(X = x) =5Cx(3/4)^(5-x)(1/4)^x(1) Probability of Getting all the spade cards:P(all the five cards should be spade) =5𝐶5(1/4)^5(3/4)^0= (1/4)^5= 1/1024(2) Probability of Getting only three spade cards:P(only three cards should be spade) =5𝐶3(1/4)^3(3/4)^2= (5!/3! 2!) × (9/1024)= 45/ 512(3) Probability of Getting no spades:P(none of the cards is a spade) =5𝐶0(1/4)^0(3/4)^5= (3/4)^5= 243/ 1024  AnsThanks
```
3 months ago
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