Conditional Probability Help

Hi, I need help with the following problems. Some clear instructions on how the problems can be solved would be extremely useful as I have limited knowledge at this time.

1. Some electronic devices are better used than new. The failure rate is higher when they are six months old. For example, half of the personal music players sold by a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 20% fail in the first six months. Yours dies after you had it for three months. What are the chances that it had this flaw?

ANSWER: 0.833, how is this answer found?

2. Patrick is flying from city A to city C with a connection in city B. The probability his first flight arrives on time is 0.25. If the flight is on time, the probability that has luggage will make the connecting flight is 0.95, but the flight is delayed, the probability that the luggage will make it is only 0.55. In either case, Patrick makes the flight. If Patrick's luggage is not there to meet him, what is the probability that Patrick was late in arriving in city B?

ANSWER: 0.964, how do i reach this answer?

rjones629 said:

Hi, I need help with the following problems. Some clear instructions on how the problems can be solved would be extremely useful as I have limited knowledge at this time.

1. Some electronic devices are better used than new. The failure rate is higher when they are six months old. For example, half of the personal music players sold by a particular brand have a flaw. If the player has the flaw, it dies in the first six months. If it does not have this flaw, then only 20% fail in the first six months. Yours dies after you had it for three months. What are the chances that it had this flaw?

Click to expand...

Imagine 1000 such devices. Half, 500, have this flaw and fail within 6 months. Half, 500, do not but then 20% of them, 20% of 500= 100, fail in the first 6 months any way. Of the 500+ 100= 600 that fail in the first 6 months, 500 of them had the flaw.

ANSWER: 0.833, how is this answer found?

2. Patrick is flying from city A to city C with a connection in city B. The probability his first flight arrives on time is 0.25. If the flight is on time, the probability that has luggage will make the connecting flight is 0.95, but the flight is delayed, the probability that the luggage will make it is only 0.55. In either case, Patrick makes the flight. If Patrick's luggage is not there to meet him, what is the probability that Patrick was late in arriving in city B?

ANSWER: 0.964, how do i reach this answer?

Click to expand...

Imagine 2000 such flights. 1/4 of them, 500, arrive on time. Of those 500, his luggage makes the connecting flight in 0.95(500)= 475 flights while in 500- 475= 25 it does not. Of the 1500 that do not arrive on time, his luggage will still get on the plane in 0.55(1500)(0.55)= 825 flights while in 1500- 825= 675 it does not. So there are 475+ 825= 1300 flights in which his luggage gets there and 675+ 25= 700 flights in which it does not. Of the 700 flights in which the luggage does not arrive, he was late in arriving in 675.

(I used the numbers, "1000" and "2000" to avoid fractions.)