Question

The probability that a bomb will hit the target is 0.8. Complete the following activity to find, the probability that, out of 5 bombs exactly 2 will miss the target.

Solution: Here, n = 5, X =number of bombs that hit the target

p = probability that bomb will hit the target = `square`

∴ q = 1 - p = `square`

Here, `X∼B(5,4/5)`

∴ P(X = x) = `""^"n""C"_x"P"^x"q"^("n" - x) = square`

P[Exactly 2 bombs will miss the target] = P[Exactly 3 bombs will hit the target]

= P(X = 3)

=`""^5"C"_3(4/5)^3(1/5)^2=10(4/5)^3(1/5)^2`

∴ P(X = 3) = `square`

Answer 1

Here, n = 5, X =number of bombs that hit the target

p = probability that bomb will hit the target = 0.8 = `bb(4/5)`

∴ q = 1 - p = `1-4/5=bb(1/5)`

Here, `X∼B(5,4/5)`

∴ P(X = x) = `""^"n""C"_x"P"^x"q"^("n" - x) = bb(""^"5""C"_x(4/5)^x(1/5)^(5-x))`

P[Exactly 2 bombs will miss the target] = P[Exactly 3 bombs will hit the target]

= P(X = 3)

=`""^5"C"_3(4/5)^3(1/5)^2=10(4/5)^3(1/5)^2`

∴ P(X = 3) = `10(4^3/5^5)`