Name CAMANO JOLINA A 2 BSAM A Date 02 16 2022 CALCULATION OF PROBABILITIES 1 47 Determine the probability p or an estimate of it for each of the following events a A king ace jack of clubs or queen of diamonds appears in drowning a single card from a well shuffled ordinary deck of cards ANSWER Let A be event of selecting a king ace jack of clubs and B be event of selecting a queen of diamonds therefore P A and P A Required probability P A U B or 3 52 1 52 3 52 1 52 4 52 1 13 b The sum 8 appears in a single toss of a pair of fair dice ANSWER The favourable cases are 2 6 3 5 4 4 5 3 6 2 therefore the p c A non defective bolt will be found next if out of 600 bolts already examined 12 were defective The number of non defective bolts are 600 12 588 then 0 98 therefore 588 600 d A 7 or 11 come up in a single toss of a pair of fair dice ANSWER the p 0 98 ANSWER Probability of getting a sum of 7 when a pair of fair dice tossed because 1 6 2 5 3 4 4 3 5 2 6 1 are the favourable outcomes and probability of getting a sum of 11 when a pair of fair dice tossed because 5 6 6 5 are the favourable outcomes Then the total probability of getting a sum of 7 and 11 2 36 on first toss therefore the p 6 36 2 36 8 36 8 36 5 36 6 36 e At least 1 head in 3 tosses of a fair coin ANSWER We can get the following possibilities HHH HHT HTH HTT THH THT TTH TTT of those 8 possibilities 7 have at least 1 head Therefore p 7 8 1 49 A marble is drawn at random from a box containing 10 red 30 white 20 blue and 15 orange marbles Find the probability that it is a orange or red b not red or blue c not blue d white e red white or blue ANSWERS a orange or red probability No of orange balls No of balls b not red or blue probability No of orange balls No of balls Total no of balls 25 75 or 1 3 Total no of balls 3 5 45 75 or 15 10 75 15 30 75 Therefore the p Therefore the p c not blue probability No of orange balls No of balls No of balls Total no of balls 15 30 10 75 or Therefore the p 55 75 11 55 11 55 d white probability No of balls Total no of balls 30 75 2 5 or Therefore the p e red white or blue probability No of balls No of balls No of balls or Therefore the p Total no of balls 20 30 10 75 60 75 4 5 4 5 3 5 1 3 2 5