Home
Class 12
MATHS
5 players of equal strength play one eac...

`5` players of equal strength play one each with each other. `P(A)=` probability that at least one player wins all matches he (they) play. `P(B)=` probability that at least one player losses all his (their) matches.

A

`P(A)=(5)/(16)`

B

`P(B)=(7)/(16)`

C

`P(AnnB)=(5)/(32)`

D

`P(AuuB)=(15)/(32)`

Text Solution

Verified by Experts

The correct Answer is:
A, B, D
`(a,b,d)` `P(A)=("^(5)C_(1)2^(6))/(2^(10))=(5)/(16)`, `P(B)=('^(5)C_(1)2^(6))/(2^(10))=(5)/(16)`
`P(AnnB)=("^(5)C_(2)xx2xx2^(3))/(2^(10))=(5)/(32)`
`implies P(AuuB)=(15)/(32)`
Promotional Banner

Topper's Solved these Questions

  • PROBABILITY

    CENGAGE|Exercise Single correct Answer|46 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PROBABILITY

    CENGAGE|Exercise Comprehension|2 Videos

  • PRINCIPLE OF MATHEMATICAL INDUCTION

    CENGAGE|Exercise Exercise|9 Videos

  • PROBABILITY AND STATISTICS

    CENGAGE|Exercise Question Bank|24 Videos

Similar Questions

Explore conceptually related problems

Sixteen players S_(1),S_(2),…,S_(16) play in a tournament. They are divided into eight pairs at random. From each pair a winner is decided on the basis of a game played between the two players decided to the basis of a game played between the two players of the pair. Assume that all the players are of equal strength. (a) Find the prabability that the player S_(1) is among the eight winners. (b) Find the probability that exactly one of the two players S_(1)and S_(2) is among the eight winners.

If a probability of a player winning a particular tennis match is 0 . 72 . What is the probabillity of the player loosing the match ?

The probability that married man watches certain TV show is 0.4 and the probabi9lity that a married woman watches the show is 0.5. the probability that a man watches the show, given that his wife dies, is 0.7. then (a)the probability that married couple watches the show is 0.35 (b)the probability that a wife watches the show given that her husband does is 7/8 (c)the probability that at least one person of a married couple will watch the show is 0.55 (d)none of these

A bag initially contains 1 red and 2 blue balls. An experiment consisting of selecting a ball at random, noting its color and replacing it together with an additional ball of the same color. If three such trials are made, then (a)Probability that a t least one blue ball is drawn is 0.9 (b)Probability that exactly one blue ball is drawn is 0.2 (c)Probability that all the drawn balls are red given that all the drawn balls are of same color is 0.2 (d)Probability that at least one red bal is drawn is 0.6

2^n players of equal strength are playing a knock out tournament. If they are paired at randomly in all rounds, find out the probability that out of two particular players S_1a n dS_2, exactly one will reach in semi-final (n in N ,ngeq2)dot

In a hurdle race a player has to cross 10 hurdles . The probability that he will clear each hurdle is 5/6. What is the probability that he will knock down less than 2 hurdles ?

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 times, the probability that the same horse wins all the three races, and the probability that a , b ,c each wins one race are, respectively. a. 8//50 ,9//50 b. 16//100 ,3//100 c. 12//50 , 15//50 d. 10//50 ,8//50

In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is (5)/(6) . What is the probability that he will knock down fewer than 2 hurdles?

Thirty two players ranked 1 to 32 are playing is a knockout tournament. Assume that in every match between any two players, the better ranked player wins the probability that ranked 1 and ranked 2 players are winner and runner up, respectively, is (A) 16/31 (B) 1/2 (C) 17/31 (D) none of these