Q28 of 30 Page 13

Assume that the probability that a bomb dropped from an airplane will strike a certain target is 0.2. If 6 bombs are dropped, find the probability that

i. exactly 2 will strike the target.


ii. at least 2 will strike the target.

We have been given that, the probability that a bomb dropped from an airplane will strike a certain target is 0.2.


Also, that 6 bombs are dropped.


Let p be the probability that a bomb dropped from an airplane will strike a certain target.


Then, q is the probability that a bomb dropped from an airplane will not strike a certain target.


⇒ p = 0.2




We know that, p + q = 1


⇒ q = 1 – p





Let X be a random variable the represents the number of bombs that strike the target.


Then, the probability that r bombs strike the target out of n bombs is given by,


P (X = r) = nCrprqn-r


Where n = 6


Let us put the values of n, p, and q in the above equation.


…(A)


(i). We need to find the probability that exactly 2 will strike the target out of 6 bombs.


Probability is given by,


Probability = P (X = 2)


So, put r = 2 in equation (A).










⇒ Probability = 0.24576


∴, the probability that exactly 2 will strike the target out of 6 bombs is 0.24576.


(ii). We need to find the probability that at least 2 will strike the target out of 6 bombs.


Probability is given by,


Probability = P (X ≥ 2)


This can also be written as,


Probability = 1 – P (X < 2)


⇒ Probability = 1 – [P (X = 0) + P (X = 1)]


Let us find the value of P (X = 0).


For this, put r = 0 in equation (A).







Now, let us find the value of P (X = 1).


For this, put r = 0 in equation (A).








Now, putting all these values in 1 – [P (X = 0) + P (X = 1)].









⇒ Probability = 0.345


∴, the probability that at least 2 will strike the target out of 6 bombs is 0.345.

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