Question
Question 7
a & b
1. (0 points) Consider a single throw of two fair dice, Determine if the events A and B are mutually exclusive Justify your answers. (a) (5 points) 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 (b) (5 points) Let A be the event that the number one face is twice the number on the other face. Let B be the event that the sum af the faces showing is a multiple of 3- 2. (15 points) 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 3 points) 3 fair dice are tossed once. A is the event that 3 shows on the first die. B is the event that 3 shows on the second die. C is the event that 3 shows on the third die. Find P(AU BUC). 4. (15 points) Suppose that P A) 0.6 P(B) 0.5 and P(An B) 02. (B) (5 points) Are A and B independent? Justify your answer. (b) (5 points) Find P A U B (e) (5 points) Find P n B) 5. 20 points 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 chipes The third um 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 um sampled? 6. 15 points) Given that P A) P(B) 0.9 P(AlB) 0.5 and P 0.4, find p(A). (10 points) a) (5 points) How many integers are between 100 and 999 (including the ends)? (b) (5 points) How many integers between 100 and 999 have distinct digits
Explanation / Answer
a)
number of integers between 100 and 999 including edges is nothing but number of 3-digit numbers possible when repetition of digits is allowed.
units and tens places can be filled in 10 possible ways(0,1,2,3,4,5,6,7,8,9)
hundreds place cannot have 0 which makes it a 2-digit number.
Total number of integers possible = 9*10*10 = 900
b)
In this case hundreds place can be filled with 9 integers.
As digits cannot repeat, tens place also 9 possible numbers.
[number used in hundreds place is excluded and 0 is included now].
units place can be filled in 8 possible ways.
[numbers excluding the digits used in hundreds and tens place]
Total number of numbers possible using distinct digits = 9*9*8 = 648
