Question

Two airplanes $I$ and $II$ bomb a target in succession. The probability of $I$ and $II$ scoring a hit correctly are $0.3$ and $0.2$, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

• A. $0.06$
• B. $0.14$
• C. $0.2$
• D. $0.7$

Answer 1

The correct option is B $0.14$

As Probability of aeroplane $I$ hitting the score correctly is $0.3$, the the probability that it does not hit the target is $1-0.3=0.7$

As Probability of aeroplane $II$ hitting the score correctly is $0.2$, the the probability that it does not hit the target is $1-0.2=0.8$

The total number of outcomes of this event are
1. When Aeroplane I hits the target successully $=0.3$
2. When Aeroplane I fails to hit the target and aeroplane II hits the target $=0.7\times 0.2=0.14$
3. When both Aeroplanes fail to hit the target $=0.7\times 0.8=0.56$

So, Probability $=\frac{NumberoffavourableOutcomes}{Totalnumberofoutcomes}=\frac{0.14}{0.3+0.14+0.56}=0.14$