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1011. Five cards are drawn successively with replacement from a well shuffled deck of 52 cards. What is the probability that
(i) all the five cards are spades?
(ii) only 3 cards are spades?
(iii) none is a spade?

Here n = 5
p = P(spade) = $13 over 52 space equals space 1 fourth comma space space straight q space equals space 1 minus straight p space equals space 1 minus 1 fourth space equals space 3 over 4$

(i) P(5 spades) = $straight C presuperscript 5 subscript 5 space open parentheses 1 fourth close parentheses to the power of 5 space equals space 1 cross times 1 over 1024 space equals space 1 over 1024$

(ii) P(3 spades) = $straight C presuperscript 5 subscript 3 space open parentheses 3 over 4 close parentheses squared space open parentheses 1 fourth close parentheses cubed space equals space straight C presuperscript 5 subscript 2 space cross times 9 over 16 cross times 1 over 64 space equals space fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction cross times 9 over 16 cross times 1 over 64 space equals 45 over 512$

(iv) P(none is a spade) = $straight P left parenthesis 0 right parenthesis space equals space straight C presuperscript 5 subscript 0 space open parentheses 3 over 4 close parentheses to the power of 5 space equals space 1 space cross times space 243 over 1024 space equals space 243 over 1024$

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1012. Find the probability of throwing at most 2 sixes in 6 throws of a single die.

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1013. The probability of a man hitting a target is

1 fourth.

He fires 7 times. What is the probability of his hitting at least twice the target?

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1014. The probability that a man hits a target when he fires is

1 fifth.

If he fires 10 rounds, what is the probability of his hitting the target at least twice?

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1015. In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is

5 over 6.

What is the probability that the will knock down fewer than 2 hurdles?

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1016. A policeman fires 6 bullets on a dacoit. The probability that the dacoit will be killed by a bullet is 0·6. What is the probability that the dacoit is still alive?

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1017. A student is given a true-false examination with 8 questions. If he gets 6 or more correct answers, he passes the examination. Given that the guesses at the answer to each question, compute the probability that he passes the examination.

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1018. An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.

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1019. Ten eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

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1020. A die is thrown 6 times. If ‘getting an odd number” is a success, what is the probability of
(i) 5 successes? (ii) at least 5 successes? (iii) at most 5 successes?

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