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Probability

Question
CBSEENMA12033896
Wired Faculty App

A coin is tossed 5 times. What is the probability of getting
(i) at least 3 heads (ii) at most 2 heads

Solution

Here n = 5,   p = P(getting head) = 1 half,     q = 1 - p = 1 - 1 half space equals space 1 half
(i) P(at least 3 heads) = P(3) + P(4) + P(5)
        equals 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 4 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 4 plus space straight C presuperscript 5 subscript 5 space open parentheses 1 half close parentheses to the power of 5 equals space open parentheses 1 half close parentheses to the power of 5 space open square brackets straight C presuperscript 5 subscript 3 space plus space straight C presuperscript 5 subscript 4 space plus space straight C presuperscript 5 subscript 5 close square brackets space equals space 1 over 32 space open square brackets fraction numerator 5 space cross times space 4 over denominator 1 space cross times 2 end fraction plus 5 over 1 plus 1 close square brackets equals space 1 over 32 left parenthesis 10 plus 5 plus 1 right parenthesis space equals space 16 over 32 space equals space 1 half
(ii) P(at most 2 heads) = 1 minus open square brackets straight P left parenthesis 3 right parenthesis space plus space straight P left parenthesis 4 right parenthesis space plus space straight P left parenthesis 5 right parenthesis close square brackets space equals space 1 minus 1 half

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