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# CALCULATION OF PROBABILITIES

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Name: CAMANO, JOLINA A. 2_BSAM-A Date: 02/16/2022CALCULATION OF PROBABILITIES1.47. 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 awell- shuffled ordinary deck of cards.ANSWER:Let A be event of selecting a king, ace, jack of clubs and B be event of selecting aqueen of diamonds, therefore;P (A) = 352 and P (A) = 152 . Required probability = P (A U B) = 352 + 152 = 452 or 113 .(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 = 536 . (c.) A non-defective bolt will be found next if out of 600 bolts already examined, 12 weredefective.ANSWER: The number of non-defective bolts are 600 – 12 = 588, then 588600 = 0.98, thereforethe p = 0.98. (d.) A 7 or 11 come up in a single toss of a pair of fair dice.ANSWER: Probability of getting a sum of 7 when a pair of fair dice tossed = 636 , because(1,6), (2,5), (3,4), (4,3), (5,2), (6,1) are the favourable outcomes, and probability ofgetting a sum of 11 when a pair of fair dice tossed = 236 , because (5,6), (6,5) arethe favourable outcomes. Then the total probability of getting a sum of 7 and 11on first toss = 636 + 236 = 836 , therefore the p = 836 .(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 = 78 . 1.49. A marble is drawn at random from a box containing 10 red, 30 white, 20 blue, and 15orange marbles. Find the probability that it is (a.) orange or red, (b.) not red or blue, (c.) notblue, (d.) white, (e.) red, white, or blue. ANSWERS:(a.) orange or red probability;No . of orangeballs+ No . of ¿ balls¿Total no . of balls → = 15+1075 = 2575 or = 13 . Therefore, the p = 13 .(b.) not red or blue probability;No . of orangeballs+ No . of ¿ balls¿Total no . of balls → = 15+3075 = 4575 or = 35 . Therefore, the p = 35 .(c.) not blue probability; No . of orangeballs+ No . of ¿ balls+ No . of ¿ balls¿Totalno .of balls → = 15+30+1075 = 5575 or = 1155 . Therefore, the p = 1155 .(d.) white probability;No . of ¿ balls¿Totalno . of balls → = 3075 or 25 . Therefore, the p = 25 .(e.) red, white, or blue probability; No . of ¿ balls + No. of ¿ balls+ No . of ¿ balls¿Total no . of balls → = 20+30+1075 = 6075 or = 45 . Therefore, the p = 45

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