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Probability

Question
CBSEENMA12033865
Wired Faculty App

A die is thrown 6 times. If ‘getting an odd number” is a success, what is the probability of
(i) 5 successes?    (ii) at least 5 successes?           (iii) at most 5 successes?

Solution

Here n = 6
p = P(getting an odd number) = P(1, 3, 5) = 3 over 6 space equals space 1 half comma space space space straight q space equals space 1 space minus space straight p space equals space 1 minus 1 half space equals space 1 half
(i) P(five successes) = P(5) = straight C presuperscript 6 subscript 5 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 5 space equals space 6 over 1 cross times open parentheses 1 half close parentheses to the power of 6 space equals space 6 space cross times 1 over 64 space equals space 3 over 32
(ii) P(at least 5 successes) = P(5) + P(6)
      equals straight C presuperscript 6 subscript 5 space open parentheses 1 half close parentheses space open parentheses 1 half close parentheses to the power of 5 space plus space straight C presuperscript 6 subscript 6 space open parentheses 1 half close parentheses to the power of 6 space equals space open parentheses 1 half close parentheses to the power of 6 space open square brackets straight C presuperscript 6 subscript 5 space plus straight C presuperscript 6 subscript 6 space close square brackets space equals space 1 over 64 left parenthesis 6 plus 1 right parenthesis space equals space 7 over 64
(iii) P(atmost 5 successes) = 

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