Question
Question 6
Consider a single throw of two fair dice. Determine if the events A and B are mutually exclusive. Justify your answers. Let A be the event that the sum of the faces showing is even. Let B be the event that the two faces showing are odd. Let A be the event that the number on one face is twice the number on the other face. Let B be the event that the sum of the faces showing is a multiple of 3. There are 10 people attending a conference talk 7 are men and 3 are women. Four of the 10 people are asked to attend another talk. What is the probability that 2 of these 4 people are women? 3 fair dice are tossed once. A is the event that 3 slows on the first die. B is the event that 3 shows on the second die. C is the event that 3 shows the third die. Find P(A Union B Union C). Suppose that P(A) - 0.6. P(B) = 0.5 and P(A Intersection B) = 0.2. Are A and B independent? Justify your answer. Find P(A^c Union B^c). Find P(A^c Intersection B). There are three urns with red and white chips. The first urn contains 4 red chips and 5 white chips. The second urn contains 2 red chips and 7 white chips. The third urn has 6 red chips and 3 white chips. One urn is chosen at random and one chip is drawn from that urn. Given that the chip drawn is red, what is the probability that the third urn was the urn sampled? Given that P(A) + P(B) = 0.9, P(A|B) = 0.5 and P(B|A) = 0.4. find P(A). How many integers are between 100 and 999 (including the ends)? How many integers between 100 and 990 have distinct digits?
Explanation / Answer
as we know that P(A|B)=P(A)*P(B|A)/P(B)
hence 0.5=0.4*P(A)/P(B)
5P(B)=4P(A)............(1)
as P(A)+P(B)=0.9
multiplying by 5
5P(A)+5P(B)=4.5
5P(A)+4P(A) =4.5
P(A)=0.5
