In a jar of ten beads, seven are red and three are blue. A bead is drawn from the jar five times with replacement. What is the probability of seeing exactly 2 blue beads?
To find the probability of seeing exactly 2 blue beads, we need to find the probability of drawing a blue bead on a single draw, and then use the binomial probability formula.
The probability of drawing a blue bead on a single draw is 3 blue beads out of 10 total beads, or 3/10.
Using the binomial probability formula, the probability of drawing exactly 2 blue beads on 5 draws is:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the total number of draws, k is the number of successful outcomes, and p is the probability of a successful outcome.
Plugging in the values, we get:
P(X = 2) = (5 choose 2) * (3/10)^2 * (1 - 3/10)^(5-2)
= (10) * (9/100) * (7/10)^3
≈ 0.1323
Therefore, the probability of seeing exactly 2 blue beads is approximately 0.1323, or 13.23%.