An unbiased coin is tossed six times. Find the probability of obtaining less than 3 heads .

Solution

Here n = 6
p = Probability of head = $1 half comma space space straight q space equals space 1 space minus space straight p space equals space 1 minus 1 half space equals 1 half$
P (less than 3 heads) = P (0) + P (1) + P (2)
$equals space straight C presuperscript 6 subscript 0 space open parentheses 1 half close parentheses to the power of 6 space plus space straight C presuperscript 6 subscript 1 space open parentheses 1 half close parentheses to the power of 5 space open parentheses 1 half close parentheses space plus space straight C presuperscript 6 subscript 2 space open parentheses 1 half close parentheses to the power of 4 space open parentheses 1 half close parentheses squared space equals open parentheses 1 half close parentheses to the power of 6 space open square brackets straight C presuperscript 6 subscript 0 space plus space straight C presuperscript 6 subscript 1 space plus space straight C presuperscript 6 subscript 2 close square brackets space equals space 1 over 64 left parenthesis 1 plus 6 plus 15 right parenthesis space equals space 22 over 64 equals space 11 over 32 space equals 0.3438$

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Probability

An unbiased coin is tossed six times. Find the probability of obtaining less than 3 heads .

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