Final answer:
To find the probability that Brian Collins clears exactly 2 hurdles out of 10, we can use the binomial probability formula. The probability of clearing a hurdle is 2/3. The probability that Brian Collins clears exactly 2 hurdles is 80/243.
Step-by-step explanation:
To find the probability that Brian Collins clears exactly 2 hurdles, we can use the binomial probability formula. The probability of clearing a hurdle is 2/3, so the probability of not clearing a hurdle is 1 - 2/3 = 1/3.
The formula for the probability of getting exactly k successes in n trials is:
P(X = k) = C(n, k) * (p^k) * ((1-p)^(n-k))
where n is the number of trials, k is the number of successes, p is the probability of success, and C(n, k) is the number of combinations of n items taken k at a time.
In this case, n = 10, k = 2, and p = 2/3.
P(clears exactly 2 hurdles) = C(10, 2) * (2/3)^2 * (1/3)^(10-2) = 45 * (4/9) * (1/3)^8 = 80/243
Therefore, the probability that Brian Collins clears exactly 2 hurdles is 80/243.