The gunner on a small assault boat fires 6 missiles at anattacking plane. Each has a 20% chance of being on target. If twoor more of the shells find their mark, the plane will crash. At thesame time, the pilot of the plane fires 10 air-to-surface rockets,each of which has a 0.05 chance of critically disabling the boat.Would you rather be on the plane or on the boat?

The gunner on a small assault boat fires 6 missiles at an attacking plane. Each has a 20% chance of being on target. If two or more of the shells find their mark, the plane will crash. At the same time, the pilot of the plane fires 10 air-to-surface rockets, each of which has a 0.05 chance of critically disabling the boat. Would you rather be on the plane or on the boat

data for the boat n =6 ; p = 20% = 0.2 ;

at least two or more find their mark the plane will crash

prob.of crash = P(X > =2) = 1-{P(X=0)+P(X =1)}

= 1-{ (0.8)6 + 6*(0.8)5 * 0.2 }

= 1-[0.262144+ 0.3932] = 0.344656

for plane n = 10 ; p = 0.05

for boat crash = P(X > =1 ) = 1- P(X =0) =1-(0.95)10 =0.4013

the prob. for the boat is high

so prefer in the plane