Exercise 2 1. A single letter is chosen at random from the alphabet. What is the probability that it is (e) P or Q? (a) B? (b) X? (c) a vowel? (d) a 5? Also, (f) what is the probability that it is not a vowel? 2. Let S represent the set of digits S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} A digit is selected at random from S. Determine the probability that it is (e) not 6. (b) greater than 6 (c) odd (d) 5 or 1 or 8 (a) 6 3. A spinner in the shape of a regular hexagon is divided into equilateral sectors. 10 The pointer is spun. What is the probability it comes to rest on 2 ,0001 0 (a 10? (b) 1? (c) a number greater than 5? 4 A roulette wheel has 37 numbers: 0, 1, 2, 3, 4, ..., 35, 36. The zero is green, half of the other numbers are red and the rest are black. A small ball is thrown onto the spinning wheel and comes to rest on one of the numbers. What is the probability that the number is (a) 24? (b) red? (c) not 24? (d) not red? SIL 5. A single card is drawn at random from a standard pack of 52 cards. Determine the probability that it is (a) the four of spades (b) a four (c) a club (d) a black card 6. Consider a sample space, S = {a, b, c, 4, 5, 6, g, h, i} Let events E1, E, and E, be E, = {a, b, c, g, h, i}= 'a letter' E2 ={4, 5, 6}= 'a number' E, = {a, i}= 'a vowel' A single element is chosen at random from S. Determine the following probabilities: (a) P(E, ) ( b ) P ( E 2 ) (c) P(E3 ) (d) P(E2 or E3) (e) P( E, or E2) (f) P(E, and E2) 7. In the year 1989, January 1 was on a Sunday. There were 52 weeks and 1 day in that year. A baby's name is selected, at random, from the 1989 birth register. Write down, as an exact fraction, the probability that the baby was born (a) after January 31, 1989. (b) on a Tuesday. (c) after 1 am, but before 5 am. (d) on a Saturday or Sunday. (e) during February. Also, (f) are you making any assumptions in your answer to, say, part (d)? 8. A standard unbiased cubical die is shown. It is rolled across the carpet and comes to rest The uppermost number is noted. List the sample points in the following events and determine their probabilities: (a) 'even number' (b) 'number greater than 4' 'even number or a number greater than 4' e 'even number and a number greater than 4