Exposure of certain fruit fly population to an insecticide has produced 2 kinds of mutations. 20% have wing mutation. 15% have eye mutation and 5% have both. A fly is selected at random. a) If it has wing mutation, what is the probability that, it also has the eye mutation? b) If it has the eye mutation, what is the probability that it has also the wing mutation? c) What is the probability that it has at least one of the mutations?

Question

Exposure of certain fruit fly population to an insecticide has produced 2 kinds of mutations. 20% have wing mutation. 15% have eye mutation and 5% have both. A fly is selected at random.  a) If it has wing mutation, what is the probability that, it also has the eye mutation?  b) If it has the eye mutation, what is the probability that it has also the wing mutation?  c) What is the probability that it has at least one of the mutations?

giskacu · Accepted Answer

Step 1  Given Information:  20% have wing mutation i.e., P(W)=0.20  15% have eye mutation i.e., P(E)=0.15  5% have both i.e., P(W and E)=P(E and W)=0.05  A fly is selected at random.  (a) If it has the wing mutation, to find the probability that it also has the eye mutation:  Conditional probability is given by the formula:  P(A∣B)=P(A and B)P(B)  Required probability is obtained as follows:  P(E∣W)=P(E and W)P(W)  =0.050.20  =0.25  Thus, if it has the wing mutation, to find the probability that it also has the eye mutation is 0.25.  Step 2  (b) If it has the eye mutation, to find the probability that it also has the wing mutation:  Using the conditional probability formula, required probability is obtained as follows:  P(W∣E)=P(W and E)P(E)  =0.050.15  =0.3333333  ≈0.33  Thus, if it has the eye mutation, to find the probability that it also has the wing mutation is 0.33   (c) To find the probability that it has at least one of the mutations:   Required probability:  P(at least one mutation)=1−P(none of the mutations)  =1−P(no wing mutation⋅no eye mutation)  =1−[(1−0.20)⋅(1−0.15)]  =1−[0.8⋅0.85]  =1−0.68  =0.32  Thus, the probability that it has at least one of the mutations is 0.32.

Exposure of certain fruit fly population to an insecticide has produce

Answered question

Answer & Explanation

New Questions in High school probability