1.(This Question Just Revises Conditional Probability.)

H-20Bayes’ Theorem

1.(This question just revises conditional probability.)

(a)Two events A and B are such that , and .

Find (i) and (ii) .

(b)C and D are independent events, with and. Find) .

(c) Two unbiased 6-sided dice are thrown. Find the following conditional probabilities:

(i) P(the total score is 8 or over  one die shows a 5)

(ii) P(one die shows a 5  the total score is 8 or over)

(iii) P(total is 6  the two dice show different scores)

(d)A bag contains ten counters number from 1 to 10. One is chosen at random. It shows an even number. Find the probability it shows a multiple of 3.

2.Where I live the probability of rain on any day is 0.3. If it is raining the probability I go for a walk is 0.2, but if it is not raining the probability I go for a walk is 0.6.

(a)Find the probability it was raining, given that I went for a walk today. (A tree diagram may help.)

(b) Yesterday I didn’t go for a walk. Find the probability that it was not raining.

3.(a)Two events A and B are such that P(A) = 0.4, P(B) = 0.8 and . Find

(b) A baker only sells brown or white bread. He knows from experience that three-quarters of his customers are women, and that the probability a woman buys brown bread is 0.6. The probability of a man buying white bread is 0.5.

A customer buys a white loaf. Find the probability that the customer is a man.

(c)80% of the time I walk to work, otherwise I take the bus. On the bus the probability I am late is 0.1, but walking the probability I am late is 0.3.

Today I was on time for work. Find the probability that I walked to work.

(d)In a class 60% of the students are boys. I know from bitter experience that while 90% of girls submit assignments on time, only 60% of boys do. I found an assignment on my desk this morning, on time. Find the probability that it was submitted by a girl.

4.A company makes glass statues. It employs three people to pack the statues into boxes. Alfredo works full-time and packs 50% of all the statues. Bob and Carla are part-time and each packs 25% of the statues.

The manager knows that the probabilities of each worker damaging a statue in packing are as follows:

A: 0.012B: 0.008C: 0.006

(a) A statue is found to have been damaged in packing. Find the probability it was packed by Alfredo.

(b) A statue is found to be undamaged in packing. Find the probability it was packed by Carla.