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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?

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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?

Here n = 4
Let p be the probability of drawing a white ball
$therefore space space straight p space equals space 5 over 20 space equals space 1 fourth comma space space space space straight q space equals space 1 minus straight p space equals space 1 minus 1 fourth space equals 3 over 4$
P(at least one ball is white) = 1 - P(0)
$equals space 1 minus straight C presuperscript 4 subscript 0 space open parentheses 3 over 4 close parentheses to the power of 4 space equals space 1 minus 1 space cross times space 81 over 256 space equals fraction numerator 256 minus 81 over denominator 256 end fraction space equals space 175 over 256.$

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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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