Question

five students are to be selected from a large population. if 60% of them are boys and the rest are girls, find the probability that: a. exactly 3 of them are boys​

Answer 1

The probability that exactly 3 out of 5 randomly selected students are boys, from a population where 60% are boys and 40% are girls, is 34.56%.

Step-by-step explanation:

The question asks to find the probability that, from a large population with 60% boys and 40% girls, exactly 3 out of 5 randomly selected students are boys. This is a probability problem that can be solved using the binomial distribution formula:

P(X = k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

• C(n, k) is the combination of n items taken k at a time.
• p is the probability of success (being a boy in this context).
• k is the number of successes (boys selected).
• n is the total number of draws (students selected).

In this example, n = 5, p = 0.60, and k = 3. We plug these into the binomial formula to calculate the probability.

The combination C(n, k) is calculated as follows:

C(5, 3) = 5! / (3! * (5-3)!) = 10

Then we calculate the probability:

P(X = 3) = 10 * (0.60)^3 * (0.40)^2

P(X = 3) = 10 * 0.216 * 0.16

P(X = 3) = 10 * 0.03456

P(X = 3) = 0.3456

Therefore, the probability that exactly 3 out of 5 students chosen at random are boys is 0.3456 or 34.56%.