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प्रश्न
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
उत्तर
Here, p = `1/6 + 1/6 + 1/6 = 1/2`
q = `1 - 1/2 = 1/2`
And n = 5
∴ P(x = r) = `""^"n""C"_"r" "p"^"r" "q"^("n" - "r")`
= `""^5"C"_3 (1/3)^3 (1/2)^(5-3)`
= `(5!)/(3!2!) * (1/2)^3 * (1/2)^2`
= `10*1/8*1/4`
= `5/16`
Hence, the required probability is `5/16`.
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