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Probability, Solved Problems Set -1, Example 1. An unbiased dice is tossed., a) Write the sample space of the experiment, b) Find the probability of getting a number greater than 4., c) Find the probability of getting a prime number., Solution:a) Sample space = {1, 2, 3, 4, 5, 6}, n(s) = 6, b) E = event of getting a number greater than 4, = {5, 6}, n (E) = 2, P (> 4) = Probability of a number greater than 4, = n(E)/n(S) = 2/6 = 1/3, c) E = Event of getting a prime number, = {2, 3, 5}, n (E) = 3, P(Prime number) = Probability of a prime number, , Example 2. A bag contains 5 red balls, 8 White balls, 4 green balls and 7 black balls. A ball, is drawn at random from the bag. Fine the probability that it is. (i) Black (ii) not green., Solution:No. of Red balls = 5, No. of White balls = 8, No. of Green balls = 4, No. of Black balls = 7, Total no. of balls = 24, (i) P (Black balls) = 7/24, (ii) P (not a green ball) = 1- P (green ball), = 1 - 4/24 = 20/24, = 5/6, , 1 of 3
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Probability, Solved Problems Set -1, Example 3. A card is drawn at random from a pack of 52 playing cards. Find the probability, that the card drawn is neither an ace nor a king., Solution:- P (neither an ace nor a king), = 1 – p (either an ace or a king), = 1 – 8/52 { no. of ace = 4, no. of king = 4, Total = 8 }, = (52 – 8)/52, = 44/52, = 11/13, Example 4. Out of 400 bulbs in a box, 15 bulbs a defective. One ball is taken out at random, from the box. Find the probability that the drawn bulb is not defective., Solution:- Total number of bulbs = 400, Total number of defective bulb = 15, Total number of non-defective bulbs = 400-15, = 385, P (not defective bulb) = 385/400, = 77/80, Example 5. Find the probability of getting 53 Fridays in a leap year., Solution:- No. of days in a leap year = 366, 366 days = 52 weeks and 2 days., A leap year must has 52 Fridays, The remaining two days can be, a., b., c., d., e., f., g., , Sunday an Monday, Monday and Tuesday, Tuesday and Wednesday, Wednesday and Thursday, Thursday and Friday, Friday and Saturday, Saturday and Sunday, , Out of 7 case, 2 cases have Friday, so, P (53 Friday) = 2/7, , 2 of 3
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Probability, Solved Problems Set -1, Example 6. Three unbiased coins are tossed simultaneously. What is the probability of, getting exactly two heads?, Solution: - When three coins are tossed simultaneously, the sample space is, S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}., n(S) = 8, E = Set of cases favorable to the event, = {HHT, HTH, THH}, n(E) = 3, P (exactly two heads) =, , Example 7. A die is thrown twice. Find the probability of getting (a) doublets (b) prime, number on each die., Solutions: - Sample space =, S = { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6), (2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6), (3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6), (4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6), (5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6), (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) }, n (S) = 36, (a) E = Events getting doublet, = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}, n (E) = 6, P(doublet) =, (b) E = Events getting prime number on each die., = {(2, 2), (2, 3), (2, 5), (3, 2), (3, 3), (3, 5), (5, 2), (5, 3), (5, 5)}, n(E) = 9;, P (getting prime number on each die) = n(E)/n(S) = 9/36 = 1/4, , 3 of 3
