1 . Weather records for WA include information about rainfall in Bunbury and Geraldton. For Bunbury, the average number of wet days each month is: N D M 4 2 F 2 A M 4 J J A S O 6 18 14 11 14 20 17 For Geraldton, the average number of wet days each month is: N F M N 2 A M A S o 4 10 14 15 13 Use relative frequency to estimate (a) the probability that it rains in Bunbury on June next year. b ) the probability that it rains in Geraldton on June next year 2. Jellybeans are packed into cellophane packets by an automatic machine. The contents of 30 packets were counted and the results recorded as shown: Number of packets 20 2 Number of jellybeans ONASKUniversity Estimate the probability that the next packet from the machine (a) contains exactly 25 jellybeans.ear (b) contains more than 25 jellybeans. 3. The game of ATwo-up'ayistoplayeda in Australian casinos. Two coins are tossed simultaneously. A record of 400 tosses was kept: 2 heads 80 96 1 tail and 1 head 192 2 tails 1 12 If the result is 1 tail and 1 head, no bets are paid. (a) Use the data to estimate the probability that on the next toss no bets are paid. If the result is 2 heads, the 'spinner' tosses the coins again. (b ) Use the data to estimate the probability that the next toss results in 2 heads. 4. A card player draws a single card from a well-shuffled deck and notes the suit. He replaces the card. After 600 trials his results were: Suit Frequency 180 141 . 156 123 When he finished, he noticed that 3 cards were missing. From this depleted pack, estimate the probability that it will be (a) a spade , POL (b) a club, (c) a black card. REC If the missing cards were all from the same suit, (d) guess the suit. Why?Exercise 2 1. is A single letter is chosen at random from the alphabet. What is the probability that it (a) B? ( b) X? Also, (c) a vowel? (d) a 5? (e) P or Q? (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 (a) 6 (b) greater than 6 (d) 5 or 1 or 8 (e) not 6. (c) odd 3. A spinner in the shape of a regular hexagon is divided into equilateral sectors. The pointer is spun. What is the probability it comes to rest on 2 10 (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 red2 SILy 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,. (nove)? (d Let events E1, E, and E, be E, = {a, b, c, g, h, i}= 'a letter' E2 = {4, 5, 6}= 'a number' E3 = {a, i}= 'a vowel' A single element is chosen at random from S. Determine the following probabilities: (a) P(E,) ( b) P ( E2 ) (c) P(E3 ) (d) P(E2 or E3) (e) P( E, or E2) (f) P(E, and E2) 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)? 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' (c ) 'even number or a number greater than 4' (d) 'even number and a number greater than 4'MATHS UNIT 2: PROBABILITY AND PROBABILITY DISTRIBUTION 2/2021 Exercise 3 1 . From a pack of 52 playing cards, one card is drawn at random. What is the probability that it is (a) the ace of spades a club (d) (c) not a club a court card (g) (e) a joker ( f ) not a joker a multiple of 3 (h) a multiple of 5 2. From a box containing 4 yellow balls, 2 green balls and 6 black balls, one ball is drawn at random. What is the probability that it is (a) a yellow ball (b) not a green ball (c) a purple ball (e) vnb.Gea either yellow, green or black ball? 3. 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 the probability of getting: (a) an odd number (b) number greater than 4 (c) even number or number greater than 4 (d) even number and a number greater than 4. 4. An impatient motorist is held up at a red traffic light. He is thinking of the next set of lights around the corner. He reasons that, since, there are 3 different coloured lights his probability of encountering a red light is 1/3. Comment on his reasoning. edi 5. There are 20 cups in the cupboard. Some are white and others are pink. The probability that a randomly selected mug is white is 0.75. How many pink cups are there? A.pathway to Monash University, 6. A woman traveling to work may choose to walk, catch the bus or use her bicycle. She is 6 times more likely to go by bus than walk but 2 times more likely to go by bus than use her bicycle. Calculate the probability that, the next time she goes to work, (a) she walks, (b) she does not walk, (c) she goes by bicycle or walks. 7. A red die and a green die are tossed. Let r represent the number of spots on the uppermost face of the red die. Let g represent the number of spots on the uppermost face of the green die. Calculate the following probabilities: (a) P(rzg) (b) P (r = 5 and r >g) (c) P(r= 5 orrzg)