`Aa n dB` play a series of games which cannot be drawn and `p , q` are their respective chance of winning a single game. What is the chance that `A` wins `m` games before `B` wins `n` games?
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Five different games are to be distributed among 4 children randomly. The probability that each child get at least one game is `1//4` b. `15//64` c. `
Correct Answer - B Total number of ways of distribution is `4^(5)`. `therefore n(S) = 4^(5)` Total number of ways of distribution so that each child gets at least one game...
2 Answers 4 views
Forty team play a tournament. Each team plays every other team just once. Each game results in a win for one team. If each team has a 50% chance of wi
Correct Answer - B Team totals must be 0, 1, 2, …., 39. Let the teams be `T_(1)T_(2),…, T_(40)`, so that `T_(i)` loses to `T_(j)` for `i lt j`. In other...
2 Answers 1 views
The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the sec
Correct Answer - A::C Let `p_(1), p_(2)` be the chances of happening of the first and second events, respectively. Then according to the given conditions, we have `p_(1) = p_(2)^(2)` and...
2 Answers 2 views
Two players `P_1`, and `P_2`, are playing the final of a chase championship, which consists of a series of match Probability of `P_1`, winning a match
`P_(1)` can win in the following matually exclusive ways: (a) `P_(1)` wins the next dix matches. (b) `P_(1)` wins five out of next six matches, so that after new six...
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Suppose the probability for A to win a game against B is 0.4. If A has an option of playing either a “best of 3 games' or a “best of 5 games match aga
Correct Answer - Fisth offer The probability `p_(1)` of winning the best of three games is equal to the sum of the probability of swimming two games and the probability of...
2 Answers 1 views
Whenever horses `a , b , c` race together, their respective probabilities of winning the race are 0.3, 0.5, and 0.2 respectively. If they race three t
Correct Answer - A `P(a)=0.3P(b)=0.5,P(c)=0.2.` Hence, a,b c are exhaustive. P(same horse wins all the three reces) =P(aaa or bbb or ccc) `=(0.3)^(3)+(0.5)^(3)+(0.2)^(3)` `=(27=125+8)/(1000)=(160)/(1000)=4/25` P(each horse wins exactly one race) =P...
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A JEE aspirant estimates that she will be successful with an `80%` chance if she studies 10 hours per day, with `60%` chance if she studies 7 hourse p
Correct Answer - C A: She gets a success T: She studies 10 h, P(T) = 0.1 S: She studies 7 h: `P(S)=0.2` F: She studies `4 h: P(F) =0.7` `P(A//T)=0.8,P(A//S)=0.6,P(A//F)=0.4`...
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A JEE aspirant estimates that she will be successful with an 80 percent chance if she studies 10 hours per day, with a 60 percent chance if she studie
Correct Answer - B A: She gets a success T: She studies 10 h, P(T) = 0.1 S: She studies 7 h: `P(S)=0.2` F: She studies `4 h: P(F) =0.7` `P(A//T)=0.8,P(A//S)=0.6,P(A//F)=0.4`...
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Football teams `T_(1)and T_(2)` have to play two games are independent. The probabilities of `T_(1)` winning, drawing and lossing a game against `T_(2
Correct Answer - B `P(XgtY)=T_(1)T_(1)+DT_(1)+T_(1)D("where"T_(1)" represents wins and D represents draw")` `=((1)/(2)xx(1)/(2))+((1)/(6)xx(1)/(2))+((1)/(2)xx(1)/(6))=5/12`
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In a game of chance a player throws a pair of dice and scores points equal to the difference between the numbers on the two dice. Winner is the person
Correct Answer - C `(c )` Player `A` can win if `A` throws `(1,6)` or `(6,1)` and `B` throws `((1,1),(2,2),(3,3),(4,4),(5,5) or (6,6))`. Thus the number of ways is `12`. Similarly the...
2 Answers 1 views