The answer is 0.432
To find the probability of selecting 2 females out of 3 students chosen at random from a class with 4 males and 6 females, we can use the binomial distribution formula:
P(X = k) = C(n, k) * p^k * q^(n-k)
where:
P(X = k) is the probability of selecting exactly k females,
C(n, k) is the number of combinations of selecting k females out of n total students,
p is the probability of selecting a female (6/10),
q is the probability of selecting a male (4/10),
n is the total number of students chosen (3), and
k is the number of females selected (2).
Substituting the values into the formula, we have:
P(X = 2) = C(3, 2) * (6/10)^2 * (4/10)^(3-2)
C(3, 2) represents the number of ways to choose 2 females out of 3, which is calculated as:
C(3, 2) = 3! / (2! * (3-2)!) = 3
Calculating further:
P(X = 2) = 3 * (6/10)^2 * (4/10)^1
P(X = 2) = 3 * (36/100) * (4/10)
P(X = 2) = 3 * 36/100 * 4/10
P(X = 2) = 432/1000
P(X = 2) = 0.432
Therefore, the probability of selecting 2 females using binomial approximation is approximately 0.432.