The local video store has determined that 65% of the store's customers are women. What is the probability that the next 3 customers will be women? Round to the nearest percent.
p = .65
(1-p) = .35
binomial distribution, n = 3
binomial coefs for n = 3 are 1, 3, 3, 1
probability of three women, zero men in three = coef(3,0)(p)^3 (1-p)^0
= 1 (.65)^3 (1)
= .2746 = 27%
Of course I made this too hard. Since it is the trivial case of all the same, not for example two men and one woman, you could just say 3 independent events each with a probability of .65 or .65^3
To find the probability that the next 3 customers will be women, we need to use the concept of independent events.
Since the probability of each customer being a woman is given as 65%, we can assume that each customer's gender is independent of the others. This means that the probability of one customer being a woman does not affect the probability of the next customer being a woman.
To calculate the probability of multiple independent events occurring, we multiply the individual probabilities together.
The probability of one customer being a woman is 65%. So, the probability of the next 3 customers all being women is:
0.65 * 0.65 * 0.65 = 0.274625
To express the probability as a percentage and round to the nearest percent, we multiply the result by 100 and round:
0.274625 * 100 ≈ 27%
Therefore, the probability that the next 3 customers will be women is approximately 27%.