Question

Eight coins are tossed together. The probability of getting exactly 3 heads is ______.

Options

• `1/256`

• `7/32`

• `5/32`

• `3/32`

Answer 1

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`