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1041. A coin is tossed 5 times. What is the probability that head appears an even number of times?

Here n = 5
$therefore space space space straight p space equals space straight P left parenthesis head space in space one space toss right parenthesis space equals space 1 half therefore space space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 half space equals space 1 half$

P(head appearing an even number of times)

$equals space straight P left parenthesis straight r space equals space 0 comma space space space 2 space or space 4 right parenthesis space equals space straight P left parenthesis 0 right parenthesis space plus space straight P left parenthesis 2 right parenthesis space plus space straight P left parenthesis 4 right parenthesis space equals space straight C presuperscript 5 subscript 0 space open parentheses 1 half close parentheses to the power of 5 minus 0 end exponent space plus space straight C presuperscript 5 subscript 2 space open parentheses 1 half close parentheses to the power of 5 minus 2 end exponent space open parentheses 1 half close parentheses squared space plus space straight C presuperscript 5 subscript 4 space open parentheses 1 half close parentheses to the power of 5 minus 4 end exponent space open parentheses 1 half close parentheses to the power of 4 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets because space straight P left parenthesis straight r right parenthesis space equals space straight C presuperscript straight n subscript straight r space straight q to the power of straight n minus straight r end exponent space straight p to the power of straight r close square brackets space equals space 1 space cross times space 1 over 32 cross times 1 plus fraction numerator 5 cross times 4 over denominator 1 cross times 2 end fraction cross times 1 over 8 cross times 1 fourth plus fraction numerator 5 cross times 4 cross times 3 cross times 2 over denominator 1 cross times 2 cross times 3 cross times 4 end fraction cross times 1 half cross times 1 over 16 equals space 1 over 32 left parenthesis 1 plus 10 plus 5 right parenthesis space equals space 16 over 32 equals space 1 half$

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1042. A coin is tossed 7 times. What is the probability that head appears an odd number of times?

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1043. A coin is tossed 7 times. What is the probability that tail appears an odd number of times?

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1044. A coin is tossed 5 times. What is the probability that head appears an odd number of times?

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1045. Past experience shows that 80 % of the operations performed by a doctor arc successful. If he performs 4 operations in a day, what is the probability that at least three operations will be successful?

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1046. Assume that on an average one telephone number out of 15 called between 2 P.M. and 3 P.M. on week days is busy. Why is the probability that if six randomly selected telephone numbers are called, at least three of them will be busy?

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1047. A bag contains 5 white, 7 red and 18 black balls. If four balls are drawn one by one with replacement, what is the probability that at least one is white?

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1048. A pair of dice is thrown 7 times. If getting a total of 9 is considered a success, what is the probability of at most 6 successes?

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1049. Five dice are thrown simultaneously. If the occurrence of an even number is considered as a success, find the probability of at the most 3 successes.

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