## Shubham Agrawal is teaching live on Unacademy Plus

Probability

About Me Shubham Agrawal IIT Roorkee 2013 graduate IIM Dropout SBI PO under 100 ranker (dropout) Left job to pursue my passion- Education

Sample Space Total number of possible outcomes. Eg Tossing a coin: 2 (H,T) Throwing a dice: 6 (1,2,3,4,5,6) Th rowing a couple of dice: 36

Mutually Exclusive If the events can't happen simultaneously. Eg. H and T in coin 1 and 2 in dice

l Equally Likely If chances of the events are same. No bias. Eg. H and T in coin 1 and 2 in dice

Independent If occurring of one event is not dependent on other. Eg. Result of first and second throw of a dice

Probability No.of events favourable to A Sample Space PCA) = 0 s P(A) s1

Probability No.of events not favourable to A Sample Space P(A)- P(A) + P(A)-1

l Odds Odds in Favour P(A)/P(A) Odds Against P(A)/P(A)

Questions Two dice are thrown simultaneously. The probability of obtaining a total score of seven 1S

Questions A bag contains 5 green and 7 red balls. Two balls are drawn. The probability that one is green and the other is red is

Questions Q. A bag contains 5 green and 7 red balls. Two balls are drawn. The probability that one is green and the other is red is GR-RG

Questions A bag contains 5 white and 7 black balls and a man draws 4 balls at random. The odds in favour of these being all black is:

Questions There are three events E1, E2 and E3. one of which must, and only one can happen. The odds are 7 to 4 against E1 and 5 to 3 against E2. The odds against E3 is .

Questions A card is drawn at random from a well shuffled pack of 52 cards. Find the probability of getting (i) a jack or a queen or a king, (ii) a two of heart or diamond (ii) !

And/Or

Concept AND OR AND-> A n B Probability will be multiplied OR -> A U B Probability will be added

S2xS) S2xsI S2xS S2 SI

Questions A man and his wife appear for an interview for two posts. The probability of the husband's selection is 1/7 and that of the wife's selection is 1/5 . The probability that only one of them will be selected is

Questions The odds against P solving a problem are 8:6 and odds in favour of Q solving the same problem are 14: 10 The probability of the problem being solved, if both of them try it, is

Questions Q. The odds against P solving a problem are 8: 6 and odds in favour of Q solving the same problem are 14: 10 The probability of the problem being solved, if both of them try it, is 1 2 6 32+44 l2x7 2 G 4 32_ L 24 424

Questions The odds against P solving a problem are 8: 6 and odds in favour of Q solving the same problem are 14: 10 The probability of the problem being solved, if both of them try it, is Q. 12 1 ceast 1 success-s 2)

Questions Q. Six dice are thrown. The probability that different number will turn up is:. 1,2 3,4,, 2D2 20 - 26 6 4 3621246 6 3 2

Questions Q. Four balls are drawn at random from a bag containing 5 white, 4 green and 3 black balls. The probability that exactly two of them are white is: 5 W,n,34 2 12 12 2

Questions Q. The probability that A can solve a problem is 2/3 and B can solve it is 3/4. If both 1S attempt the problem, what is the probability that the problem gets solved?

Questions Q. The probability that A can solve a problem is 2/3 and B can solve it is 3/4. If both attempt the problem, what is the probability that the problem gets solved? lA)-213 3 14

Questions Q. Three integers are chosen at random from the first 20 integers. The probability that their product is even, is

Questions Q. A die is loaded in such a way that each odd number is twice as likely to occur as each even number. If E is the event of a number greater than or equal to 4 on a single toss of the die, then P(E) is:

Questions Q. A and B are two independent events. The probability that both A and B occur is 1/6 and the probability that neither of them occurs is 1/3. The probabiljty of occurrence of A is. 6PIA) 2. 0

Questions Q. In each of a set of games it is 2 to 1 in favour of the winner of the previous game. The chance that the plaver who wins the first game shall win three at least of the next four is 2 33 3 33 33 23