Reference no: EM13277514

1. Show that 2ⁿ - ( n+1 ) equations are needed to establish the independence of n events.

2. Box 1 contains 1 white and 999 red balls. Box 2 contains 1 red and 999 white balls. A ball is picked from a randomly selected box. If the ball is red what is the probablity that it came from box 1?

3. Box 1 contains l000 bulbs of which 10 percent are defective. Box 2 contains 2000 bulbs of which 5 percent are defective. Two bulbs are picked from a randomly scitivted box. (a) in the probability that both bull's arc defective, (h) Assuming that both are defective, find the probability that they came from box I.

4. A train and a bus arrive at the station at random between 9 A.Nt and 10 A.M. The train stops for 10 minutes and the bus for x minutes.

Find x so that the probability that the bus, and the train will meet equals 0.5.

5. We have two coins the first is fair and the second two-headed. we pick one of the coins at random. we loss toss it twice and heads shows both times. Find the probability that the coin picked is fair.

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