Answer to Question #180361 in Statistics and Probability for Yahya

Question

The probability of a man hitting a target is 0.40. If he fires 5 times then, find the probability of hitting the target, (a) exactly 3 times, (b) at least 4 times

Answer 1

p=0.4,q=1-p=0.6

n=5

(a) P(exactly three times)= $^5C_3(0.4)^3(0.6)2=10\times 0.4^3\times 0.36=0.2304$

(b) P( at least 4 times)=$P(r\ge 4)=P(r=4)+P(r=5)=^5C_4(0.4)^4(0.6)+^5C_5(0.4)^5$

$=3\times (0.4)^4+(0.4)5=0.08704$