Question

Suppose that in a certain population of lizards under a particular set of environmental conditions, the probability of obtaining a male is 2/3. Assume that the sexes of each individual are independent. What is the probability of obtaining exactly two males in a clutch of three? (Note: there are three ways of obtaining exactly two males, depending on birth order)

Answer 1

The probability of obtaining exactly two males in a clutch of three lizards, given that the probability of a male is 2/3, is calculated using the binomial formula to be 4/9 or approximately 0.4444.

Step-by-step explanation:

The question involves calculating the probability of obtaining exactly two males in a clutch of three lizards where the probability of obtaining a male is 2/3. Since the sexes of individual lizards are independent, the probability of this event can be computed using the binomial probability formula, which in this case is: P(X = 2) = 3 * (2/3)^2 * (1/3)^1, where X is the random variable representing the number of males.

Using the binomial probability formula, the calculation proceeds as follows:

The number of ways to choose 2 males out of 3 is given by the binomial coefficient: 3C2 = 3

The probability of each individual being male is 2/3

The probability of one individual being female (since it's the complement of being male) is 1/3

Thus, the desired probability is 3 * (2/3)^2 * (1/3) = 4/9 or approximately 0.4444

Answer 2

4/9

Step-by-step explanation:

Given;

As given, probability of obtaining a male is = 2/3;

sexes of each individual are independent.

Probability of obtaining two males in cluster of three is;

2/3* 2/3= 4/9

So the probability of obtaining two males in cluster of three is= 4/9

There are three ways of calculation.