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Question
Eight coins are tossed together. The probability of getting exactly 3 heads is ______.
Options
`1/256`
`7/32`
`5/32`
`3/32`
Solution
Eight coins are tossed together. The probability of getting exactly 3 heads is `7/32`.
Explanation:
Here, n = 8
p = `1/2`
q = `1 - 1/2 = 1/2`
And r = 3
We know that P(x = r) = `""^"n""C"_"r" "p"^"r" . "q"^("n" - "r")`
∴ P(x = 3) = `""^8"C"_3 (1/2)^3 (1/2)^(8 - 3)`
= `(8!)/(3! 5!)*(1/2)^3 (1/2)^5`
= `56*(1/2)^8`
= `56*1/256`
= `7/32`
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