Question

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring?

Answer 1

Answer:

The probability that non of the customers return a ring is 0,59

Explanation:

According to their records, 10% of the rings are returned. This means 1 of every 10 rings are returned.

$\frac{1}{10} = 0,1$

This also means that 9 of 10 every rings are not returned.

$\frac{9}{10}=0,9$

5 different customers (C1, C2, C3, C4, C5) buy a wedding ring = those are independents events, which means that the return of the ring by one customer has no effect on the probability that another customer will also return it.

P(C1 ∩ C2 ∩ C3 ∩ C4 ∩ C5) = P(C1)P(C2)P(C3)P(C4)P(C5)

0,9 X 0,9 X 0,9 X 0,9X 0,9 = $0,9^{5}$ = 0,59

Answer 2

The probability that none of the customers return a ring is 59%

Explanation:

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10% of the diamond wedding rings are returned. Five different customers buy a wedding ring. What is the probability that none of the customers return a ring?

Probability is the numerical description about how likely an event is occur or how likely it is that a proposition is true. Binomial probability is the probability of exactly $x$ successes on $n$ repeated trials in an experiment which has two possible outcomes

10% of diamond wedding rings are returned, therefore the probability that any given ring will be returned is 10%.  Whereas the probability that a ring won't be returned is 90%.  The probability that all five customers will not return their rings is 0.9 to the fifth power.

The binomial probability. The probability of getting r successes out of n trials, where the probability of success of each trial is p and the probability of failure of each trial is q, where q=1-p is given by

$\frac{n!(\rho_r)(q_{n-r})}{r!(n-r)!}$

$n=5, r=0, p=0.10$ and $q=0.9$

Therefore we have

$\frac{5!(0.1_0)(0.9_5)}{0!5!}= 0.590$

$0.9^5 = 0.59$ or $(\frac{9}{10})^7$

Therefore there is probability of 59% that none of the rings will be returned.

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