Question

A nunclear missile is fired from the ship.The probability of it being detected by radar is $\frac{1}{3}$.The probability that the missile hits the target given that it went unnoticed is $\frac{3}{4}$.If 4 missiles are targeted from the ship then the probability that all 4 hit the target is.

• A. 2/8
• B. 3/16
• C. 1/16
• D. 1/3

Answer 1

The correct option is C

1/16

P(Missile detected)=P(A)=$\frac{1}{3}$

P(A')=$\frac{2}{3}$

$P\left(\frac{S}{A^{\prime }}\right)=\frac{3}{4}$

P(S)=Hitting the target= P(S intersection A)+P(S intersection A')

$P\left(S\right)=P\left(S\right).P\left(\frac{S}{A}\right)+P\left(S\right)\times P\left(\frac{S}{A^{\prime }}\right)=\left(\frac{1}{3}\right)\times 0+\left(\frac{2}{3}\right)\times \frac{3}{4}=\frac{2}{4}=\frac{1}{2}$

P(SSSS)=P(All hitting the target)=$(\frac{1}{2}{)}^4=\frac{1}{16}$