Question

11. In a bombing action there is 50% chance that any bomb will strike the target. Two direct hits are needed to destroy
the target completely. How many bombs are required to be dropped to give a 99% chance or better of completely
destroying the target.​

Answer 1

Step-by-step explanation:

The probability of success in one strike is p=

2

1

.

⇒ Probability of failure =q=

2

1

Now, probability of r successes P(x=r)=

n

C

r

.(

2

1

)

r

.(

2

1

)

n−r

=

n

C

r

(

2

1

)

n

According to the given condition, P(x≥2)≥0.99

⇒1−P(x<2)≥0.99

⇒1−P(x=0)−P(x=1)≥0.99

⇒1−0.99≥

2

n

1+n

⇒2

n

≥100+100n

For n=10, 2

n

<100+100n

For n=11,12,13,

2

n

>100+100n.