In a department store there are 120 customers, 90 of whom will buy at least 1 item. If 5 customers are selected at random, one by one, find the probability that all will buy at least 1 item.
the answer the book is 243/1024
Pr=(90/120)(89/119)(88/118)(87/117)(86/116)
Great, we agree. Put (90/120)(89/119)(88/118)(87/117)(86/116) in your google search window.
90/120)(89/119)(88/118)(87/117)(86/116
Well, let's do some clown math!
Out of the 120 customers, 90 will buy at least 1 item, which means 30 of them won't buy anything.
To find the probability that all 5 customers will buy at least 1 item, we need to calculate the probability of each customer buying something and then multiply them together.
For the first customer, the probability of buying an item is 90/120, which simplifies to 3/4.
For the second customer, since the first customer has already bought something, there are now 119 customers left, with 89 of them willing to buy. So the probability is 89/119, which simplifies to 11/17.
For the third customer, there are now 118 customers left, with 88 of them willing to buy. So the probability is 88/118, which simplifies to 22/29.
For the fourth customer, there are now 117 customers left, with 87 of them willing to buy. So the probability is 87/117, which simplifies to 29/39.
For the fifth customer, there are now 116 customers left, with 86 of them willing to buy. So the probability is 86/116, which simplifies to 43/58.
To find the overall probability, we need to multiply all these probabilities together.
(3/4) * (11/17) * (22/29) * (29/39) * (43/58) = 0.0960 (rounded to four decimal places)
So, the probability that all 5 customers will buy at least 1 item is approximately 0.0960, or about 9.60%.
But remember, this is clown math, so take it with a clown-sized grain of salt!
To find the probability that all 5 randomly selected customers will buy at least 1 item, we need to calculate the probability of each customer buying at least 1 item and then multiply those probabilities together.
First, let's calculate the probability of one customer buying at least 1 item. We are given that out of the 120 customers, 90 will buy at least 1 item. So, the probability of one customer buying at least 1 item is 90/120 = 3/4.
Since each customer is selected one by one, we need to multiply the probabilities of all 5 customers buying at least 1 item. Therefore, the probability that all 5 customers will buy at least 1 item is (3/4) * (3/4) * (3/4) * (3/4) * (3/4) = (3/4)^5 = 243/1024.
Therefore, the probability that all will buy at least 1 item is 243/1024.