An anti- aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
Choose the correct choice from the following answers.
A) 0.6872  B) 0.4379  C) 0.6976  D) 0.1274  E) None of these
Solution:   Required probability:   =(0.4Ã—0.7Ã—0.8Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.9)+(0.6Ã—0.7Ã—0.2Ã—0.9)+(0.6Ã—0.7Ã—0.8Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.9)+(0.4Ã—0.7Ã—0.2Ã—0.9)+(0.4Ã—0.7Ã—0.8Ã—0.1)+(0.6Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.8Ã—0.1)+(0.6Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—0.9)+(0.6Ã—0.3Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.8Ã—0.1)+(0.4Ã—0.7Ã—0.2Ã—0.1)+(0.4Ã—0.3Ã—0.2Ã—0.1)   =0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002   =0.6976   ANSWER IS 0.6976
<result>C</result>
An anti- aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the first, second, third and fourth shots are 0.4, 0.3, 0.2 and 0.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?