In a shop there are 20 customers, 18 of whom will make a purchase. If three customers are selected, one at a time, at random, what is the probability that all will make a purchase?
0.7717
0.7157
0.8524
0.8808
To find the probability that all three selected customers will make a purchase, we need to use the concept of probability.
First, let's calculate the probability of one customer making a purchase. Out of the 20 customers, 18 will make a purchase, so the probability of one customer making a purchase is:
P(1 customer making a purchase) = 18/20 = 0.9
Now, when selecting customers one at a time, the events of each selection are independent (meaning one customer's decision does not affect the others), so we can multiply the probabilities together to find the probability that all three selected customers will make a purchase:
P(all three customers making a purchase) = P(1st customer making a purchase) * P(2nd customer making a purchase) * P(3rd customer making a purchase)
Since these probabilities are independent, we can multiply them:
P(all three customers making a purchase) = 0.9 * 0.9 * 0.9
Calculating this gives us:
P(all three customers making a purchase) = 0.729
So, the correct answer is not one of the given options. It should be 0.729.