Question

The X7 allele in a species of a plant has 75 percent penetrance for producing red spots and 60 percent penetrance for dwarfism. If these probabilities of penetrance are independent, _______ percent of individuals with the X7 allele will have neither red spots nor will be dwarfs.

Answer 1

10 percent

Explanation:

Recall that,

Probability of an event = number of favorable outcome / number of total possible outcome.

and that ;

• Independent events are events in which the probability of the occurrence of one does not in any way affect the probability of the other event occurring. An example of two independent events is as follows; say you rolled a die and flipped a coin. The probability of getting any number face on the die in no way influences the probability of getting a head or a tail on the coin.

The percentage penetrance for producing red spots is 75%, hence the probability = 75/100= 0.75

The percentage penetrance for dwarfism is 60%, hence the probability= 60/100= 0.60

let P(A) represent the probability of penetrance for producing red spots = 0.75

let P(B) represent the probability of penetrance for dwarfism = 0.60

Recall that : the probability that an event will occur = 1 - probability that the event will not occur.

let P(A') represent the probability that there will be no red spots= 1- P(A)= 1 - 0.75 = 0.25

let P(B') represent the probability that there will be no dwarf= 1- P(B)= 1 - 0.6 = 0.4

the probability of individuals with X7 allele that will have neither red spots nor will be dwarfs. = P(A') × P(B')= 0.25 × 0.4 = 0.1

In percent the answer will be 0.1 × 100= 10 percent