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Probability

Short Answer Type

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

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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?

Here n = 5
p = P(head) = $1 half comma space space space straight q space equals space 1 minus 1 half space equals space 1 half$
P(head appears an odd number of times) = P(1) + P(3) + P(5)
$equals space straight C presuperscript 5 subscript 1 space open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses space plus space straight C presuperscript 5 subscript 3 space open parentheses 1 half close parentheses squared space open parentheses 1 half close parentheses cubed space plus space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 space equals space open parentheses 1 half close parentheses to the power of 5 space open square brackets straight C presuperscript 5 subscript 1 space plus space straight C presuperscript 5 subscript 3 space plus space straight C presuperscript 5 subscript 3 close square brackets space equals space 1 over 32 open square brackets 5 over 1 cross times fraction numerator 5 cross times 4 over denominator 1 cross times 2 end fraction plus 1 close square brackets space equals 1 over 32 left square bracket 5 plus 10 plus 1 right square bracket space equals space 16 over 32 equals space 1 half$

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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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1050. A die is thrown 6 times and getting a multiple of 3 is a success. Find the probability of getting at most 5 successes.

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