Question

1000 caterpillars are divided at random into 2 lots of 500 caterpillars each. Then one lot is sprayed with zap and the other lot with zoom. Of those sprayed with zap, 400 caterpillars were killed, and those sprayed with zoom , 450 were killed. Suppose a caterpillar is selected at random, what is the probability that it was sprayed with zap. B) what is the probability that it was killed? C) what is the probability that it was killed given it was sprayed with zap, d( are the events zap and killed independent

Answer 1

let events as,

$K=killed\ caterpillars\\ Z_1=sprayed \ with\ zap\\ Z_2=sprayed\ with\ zoom\\$

a)  The probability that caterpillar was sprayed with zap,

$P(Z_1)=\frac{Zap\ sprayed\ caterpillars}{All\ caterpillars}\\ P(Z_1)=\frac{500}{1000}\\ P(Z_1)=0.5\\$

b) The probability that caterpillar was killed,

$P(K)=\frac{All\ killed\ caterpillars}{All\ caterpillars}\\ P(K)=\frac{850}{1000}\\ P(K)=0.85\\$

c) The probability that caterpillar was killed given it was sprayed with zap

$P(K|Z_1)=\frac{number \ of\ sampes(K\cap Z_1)}{number \ of\ samples\ event(Z_1)}\\ P(K|Z_1)=\frac{400}{500}\\ P(K|Z_1)=0.8$

d) The Killed event and Zap event is dependent. Because

$P(K|Z_1) \not = P(K)$ according to part (b) & (c)