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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?

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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.

Here n = 6
Now, p + q = 1 and p = 2q
$therefore space space space 2 space straight q plus straight q space equals space 1 space space space rightwards double arrow space space space space straight q space equals space 1 third comma space space space therefore space space space space straight p space equals space 2 over 3.$

$therefore$ P(at least 4 successes in 6 trials) = $straight P left parenthesis straight X greater or equal than 4 right parenthesis space equals space straight P left parenthesis 4 right parenthesis space plus space straight P left parenthesis 5 right parenthesis space plus space straight P left parenthesis 6 right parenthesis$

$equals space straight C presuperscript 6 subscript 4 space straight q squared space straight p to the power of 4 plus space straight C presuperscript 6 subscript 5 space straight q space straight p to the power of 5 space plus space straight C presuperscript 6 subscript 6 space straight p to the power of 6 equals space straight p to the power of 4 space open square brackets straight C presuperscript 6 subscript 2 space end subscript straight q squared space plus space straight C presuperscript 6 subscript 1 space straight p space straight q space plus space straight C presuperscript 6 subscript 0 space straight p squared close square brackets equals space open parentheses 2 over 3 close parentheses to the power of 4 space open curly brackets fraction numerator 6 cross times 5 over denominator 1 cross times 2 end fraction open parentheses 1 third close parentheses squared space plus space 6 over 1.2 over 3.1 third plus 1 space cross times space open parentheses 2 over 3 close parentheses squared close curly brackets equals space 16 over 81 open curly brackets 15 over 9 plus 12 over 9 plus 4 over 9 close curly brackets space equals space 16 over 81 cross times 31 over 9 space equals 496 over 729.$

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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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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.