the participants in a television quiz show are picked from a large pool of applicants with approximately equal number of men and women.Among the last 11 participant there have been only 2 women.If participants are picked randomly,what is the probability of getting 2 or fewer women when 11 people are picked
.032 maybe
the answer is actually 0.33!!
oh wait sorry my bad i meant to put 0.033 lolll
To calculate the probability of getting 2 or fewer women when 11 people are picked randomly from a pool with an equal number of men and women, we need to use the concept of binomial probability.
Here's how you can calculate it step-by-step:
Step 1: Determine the probability of getting a woman (p) in one pick. Since there is an equal number of men and women, the probability of picking a woman is 1/2 or 0.5.
Step 2: Determine the total number of picks (n), in this case, 11.
Step 3: Calculate the probability of getting exactly 2 women out of 11 picks using the binomial probability formula:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
Where:
P(X = k) is the probability of getting exactly k women
(n choose k) represents the number of ways to choose k items from a set of n items and can be calculated using combinations: (n choose k) = n! / (k! * (n - k)!)
p is the probability of getting a woman (0.5)
k is the number of women (in this case, 2)
n - k is the number of men (in this case, 11 - 2 = 9)
So, P(X = 2) = (11 choose 2) * 0.5^2 * 0.5^9
Step 4: Calculate the probability of getting fewer than 2 women by adding the probabilities of getting exactly 0 women and exactly 1 woman to the probability of getting exactly 2 women.
P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)
Now let's calculate the probabilities:
P(X = 0) = (11 choose 0) * 0.5^0 * 0.5^11 = 1 * 1 * 0.00048828125 = 0.00048828125
P(X = 1) = (11 choose 1) * 0.5^1 * 0.5^10 = 11 * 0.5 * 0.0009765625 = 0.00537109375
P(X = 2) = (11 choose 2) * 0.5^2 * 0.5^9 = 55 * 0.25 * 0.001953125 = 0.027099609375
P(X ≤ 2) = 0.00048828125 + 0.00537109375 + 0.027099609375 ≈ 0.032959
Therefore, the probability of getting 2 or fewer women when 11 people are randomly picked is approximately 0.032959 or 3.3%.