EXPERIMENT: Experiment is Definite/Countable probable results Example: Tossing a coin Throwing a dice OUTCOMES: Outcomes is probable results related to an experiment Example: H, T Coin 1, 2, 3, 4, 5, 6 Dice SAMPLE SPACE: Sample space is total no. of outcomes/set of all possible outcomes related to an experiment Example: { H, T } { 1, 2, 3, 4, 5, 6 } PROBABILITY OF AN EVENT [ P(E) ]: P(E) No. of favourable outcomes SURE EVENT: Total no. of outcomes No. of favourable outcomes No.of total outcomes P(E) 1 IMPOSSIBLE EVENT: 1 No outcome satisfies the event i. e P(E) 0 COMPLEMENTARY EVENT [ P(E) ]: P(E ) 1 P(E) i. e P(E) + P(E ) 1 0 P(E) 1 SAMPLE SPACE: 1 Tossing one coin 2 { H, T } 2 Tossing two coins 2 2 4 { HT, TH, HH, TT } 3 Tossing three coins 2 3 8 { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } 4 Tossing four coins 2 4 16 { } 5 Tossing/throwing a Dice 6 { 1, 2, 3, 4, 5, 6 } 6 Tossing/throwing two Dice 6 2 36 { (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) } 7 Tossing/throwing three Dice 6 3 216 { }
8 Throwing a Coin & Dice together 2 6 12 PACK OF CARDS (PLAYING CARDS): Total playing cards 52 Total different cards (13) Ace (A) 2 3 4 5 6 7 8 9 10 Jack (J) Queen (Q) King (K) 52 playing cards divided into 4 sets Hearts 13 cards Red color Diamonds 13 cards Red color Spades 13 cards Black color Clubs 13 cards Black color FACE CARDS: Jacks, Queens and Kings are called Face Cards because the cards pictures of their names There are 12 face cards n cr n! (n r)! r! n cr n cn r n cn 1 n c0 1 10 C2 10! (10 2)! 2! 10! 8! 2! 10 9 8! 8! 2 10 9 2 45 (answer) 1 A bag contains 6 white, 4 black balls. Two balls are drawn at a random. Find the possibility that they are the same color. n(s) 6 + 4 10 C2 N(E) (2 white balls out of 6) or (2 black ball out of 4)
6 C2 + 4 C2 21 Therefore, P(E) 21 45 7 15 (answer) 2 A card is drawn from a pack of 52 cards. The probability of getting a queen of club or king of heart is.. N(S) 52 Let E event of getting a queen of club or king of heart Then, N(E) 2 Therefore, P(E) 2 52 1 26 (answer) 3 One card is drawn from a pack of 52 cards. What is the probability that the card drawn is either red or a king.. N(s) 52 There are 26 red cards (including 2 kings) & there are two more kings Let E event of getting a red car or king N(E) 28 Therefore, P(E) 28 52 7 13 (answer) 4 A box contains 5 green, 4 yellows and 3 white marbles. 3 marbles are drawn random. What is the probability that they are not the same color.. N(S) 5 + 4 + 3 12 C3 220 Let E event of drawing (3 marbles out of 5) or (3 marbles out of 4) or (3 marbles out of 3) 5 C2 + 4 C2 + 3 C2 15
Therefore, P(E) 15 / 220 3 44 1 3 44 41 (answer) 44 5 A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the ball drawn is blue N(S) 2 + 3 + 2 7 C2 21 Let N(E) No. of ways drawing 2 ballsout oof (2+3) 5 C2 10 Therefore, P(E) 10 21 (answer) 6 A box contains 4 green, 3 red and 6 blue pens. If two pens are picked at random. What is the probability that they are different color. Total no. of ways 2 pens selected from the 13 (4+3+6) pens N(S) 13 C2 78 No. of ways two different colour pes are selected is P(E) 4 C1 3 C1 + 3 C1 6 C1 + 6 C1 4 C1 54 Therefore, P(E) 54 78 9 13 (answer) 7 In a lottery 10,000 tickets are sold and ten prizes are awarded. What is the probability of not getting a prize if you buy one ticket.. Probability of winning on buying one lottery ticket 10 C1 10000 C1 1 1000
Therefore, required probability 1 1 1000 999 (answer) 1000 Fdaytalk.com 8 A speaks the truth 3 out of 4 times and B, 5 out of 6 times. What is the probability that they will contradict each other in starting the same fact. The probability that A speaks truth 3 4 The probability that A lies 1 3 4 1 4 The probability that B speaks truth 5 6 The probability that B lies 1 5 6 1 6 Both are contradictory, therefore, one will speak truth and other lie Therefore, required probability 3 4 1 6 + 1 4 5 6 1 3 (answer) 9 In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize (getting a prize) 10 10 + 25 2 (answer) 7 10 If the probability of police ride on any given day in the house of a criminal is 50%, then what is the probability that is the police raid on exactly 3 days in 5 day period Probability that the house could be raided on any day in 5 days period 1 2 1 2 1 2 1 2 1 2 1 32 5 C3 1 32 5 16 (answer) 11 Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that both of them are either red or king..
26 C 2 + 4 C2 2 C2 52 C2 55 221 (answer) 12 A book contains 1000 pages. A page is chosen at random. The probability that the sum of the digits of the marked number on the page is equal to 9. The no. of numbers whose sum is 9 One digit numbers 1 Two digit numbers 9 Three digit numbers 9 + 8 + 7 + + 1 45 Therefore, required probability 1+9+45 1000 11 200 (answer) 13 A company CEO wants to visit four plants P, Q, R and S on the official trip. The probability that he visits Q just before R is Let QR as one unit 3! 4! 1 4 (answer) 14 Four boys and three girls stand in queue for an interview. The probability that they stand in alternate position is.. Total no. of possible arrangements for 4- boys and 3- girls in a queue 7! When they occupy alternate position, then the arrangement would be like BGBGBGB Thus, total no. of possible arrangements 4! 3! Therefore, required probability 4! 3! 7! 1 35 (answer) 15 The probability that a man will be alive for 10 more years is 1/4 and the probability that his wife will alive for 10 more years is 1/3. The probability that none of them will be alive for 10 more years is
(1 1 4 ) (1 1 3 ) 1 2 (answer) 16 Ram and Shyam appear for an interview for two vacancies in an organization for the same post. The probabilities of their selection are 1 6 and 2 5 respectively. What is the probability that at least one of them will be selected? 1 (1 1 6 ) (1 2 5 ) 1 5 6 3 5 1 2 (Answer) 17 A person has 12 friends of whom 8 are relatives. In how many ways can he invite 7 friends such that at least 5 of them may be relatives? No. of ways 8c 5 4c 2 + 8c 6 4c 1 + 8c 7 8 7 6 3 2 4 3 2 456 (answer) + 8 7 2 4 + 8 18 P, Q and R shoot to hit a target. If P hits the target 4 times in 5 trials, Q hits it 3 times in 4 trials and R hits it 2 times in 3 trials. What is the probability that the target is hit by at least 2 persons? P 4 5 and P 1 5 Q 3 4 and Q 1 4 R 2 3 and R 1 3 PQR + PQ R + P QR + PQR 4 5 3 4 1 3 + 4 5 1 4 2 3 + 1 5 3 4 2 3 + 4 5 3 4 2 3 5 6 (answer)
18 Two dice are thrown simultaneously. The Probability of obtaining a total score of seven is. Favourable conditions are (6, 1), (5, 2), (4, 3), (3, 4), (2, 5), (1, 6) Total possible cases are 6 6 36 Favourable cases Required Probability Total possible cases 6 36 1 6 (answer) 19 In a container there are 28 eggs out of which 8 eggs are rotten. If two eggs are chosen at random, what will be the probability that atleast one egg is rotten. Required combination (1 rotten egg and 1 good egg) or (2 rotten eggs) 8 C1 20 C1 + 8 C2 8 20 + 28 188 188 20 C 2 188 14 27 94 189 (answer)