Question

REGULARITY A group of 10 choir members are selected at random to perform solos. If there are an equal number of boys and girls in the choir, find the probability of the choir members selected being 7 boys and 3 girls. Round to the nearest percent if necessary.

Answer 1

Using the binomial probability formula, the probability of selecting 7 boys and 3 girls out of 10 choir members is 0.1171875, or 11.72%.

The binomial probability formula is:

`P(x) = (n choose x) * (p^x) * (1-p)^(n-x)`

Where:

The total number of trials = n

The number of successful trials = x

The probability of success on each trial = p

n = 10

x = 7 boys and 3 girls

p = 0.5.

Using the binomial probability formula, the probability of selecting 7 boys and 3 girls out of 10 choir members is:

`P(7 boys and 3 girls) = (10 choose 7) * (0.5^7) * (0.5^3)`

Calculating (10 choose 7) = 120, and simplifying the equation:

P(7 boys and 3 girls) = 120 * 0.0078125 * 0.125 = 0.1171875

Thus, the probability of selecting 7 boys and 3 girls out of 10 choir members is 0.1171875, or 11.72%.