A coin is tossed 5 times. What is the probabilities of obtaining at least 2 tails?

Solution

Here n = 5
Let p be the proability of getting a tail
$therefore space space space straight p space equals space 1 half comma space space straight q space equals space 1 minus straight p space equals 1 minus 1 half space equals 1 half$
P(at least 2 tails) = 1 - $open square brackets straight P left parenthesis 0 right parenthesis space plus space straight P left parenthesis 1 right parenthesis close square brackets$
$equals space 1 minus open square brackets straight C presuperscript 5 subscript 0 space open parentheses 1 half close parentheses to the power of 5 plus space straight C presuperscript 5 subscript 1 open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses space close square brackets space equals space 1 minus space open parentheses 1 half close parentheses to the power of 5 space left square bracket space 1 plus 5 right square bracket space equals space 1 minus 6 over 32 space equals 1 minus 3 over 16 space equals 13 over 16$

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Probability

A coin is tossed 5 times. What is the probabilities of obtaining at least 2 tails?

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