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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?

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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?

Here n = 4
$straight p space equals space 80 over 100 space equals space 4 over 5 comma space space space space straight q space space equals 1 space minus space straight p space equals space 1 minus 4 over 5 space equals space 1 fifth$
P(at least three successful operations) = P(3) + P(4)
$equals space straight C presuperscript 4 subscript 3 space open parentheses 1 fifth close parentheses space open parentheses 4 over 3 close parentheses cubed space plus space straight C presuperscript 4 subscript 4 space open parentheses 4 over 5 close parentheses to the power of 4 space equals 4 over 1 cross times 1 fifth cross times 64 over 125 plus 1 cross times 256 over 625 equals space 256 over 625 plus 256 over 625 plus 512 over 625 equals space 0.8192.$

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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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