Sixteen players P1.P2.………P16 play in a tournament.

Sail E0 Webinar

Question

Sixteen players

P_{1} . P_{2} . \dots \dots \dots P_{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 of the pair.Assuming that all the players are of equal strength, the probability that exactly one of the two players

P_{1}

and

P_{2}

is among the eight winners is

Options:

A . 415

B . 715

C . 815

D . 1730

Answer: Option C
:
C
Let

E_{1} (E_{2})

denote the event that

P_{1}

and

P_{2}

are paired (not paired) together and let A denote the event that one of two players

P_{1}

and

P_{2}

is among the winners.
Since, P1 can be paired with any of the remaining 15 players.
We have,

P (E_{1}) = \frac{1}{15}

and

P (E_{2}) = 1 - P (E_{1}) = 1 - \frac{1}{15} = \frac{14}{15}

In case

E_{1}

occurs, it is certain that one of

P_{1}

and

P_{2}

will be among the winners. In case

E_{2}

occurs, the probability that exactly of

P_{1}

and

P_{2}

is among the winners is

P {(P_{1} \cap_{2}) \cup (_{1} \cap P_{2})} = P (P_{1} \cap_{2}) + P (_{1} \cap P_{2}) = P (P_{1}) P (_{2}) + P (_{1}) P (P_{2}) = (\frac{1}{2}) (1 - \frac{1}{2}) + (1 - \frac{1}{2}) (\frac{1}{2}) = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}

ie,

P (\frac{A}{E_{1}}) = 1

and

P (\frac{A}{E_{2}}) = \frac{1}{2}

By the total probability Rule,

P (A) = P (E_{1}) . P (\frac{A}{E_{1}}) + P (E_{1}) . P (\frac{A}{E_{2}}) = \frac{1}{15} (1) + \frac{14}{15} (\frac{1}{2}) = \frac{8}{15}

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. In four schools B1,B2,B3,B4 the percentage of girls students is 12, 20, 13, 17 respectively. From a school sel....a girl. The probability that the school selected is B2, is

Question 2. The probability that A speaks truth is 45, while this probability for B is 34. The probability that they contradict each....each other when asked to speak on a fact is

Question 3. Ashu studies at Byju's classes and her probability of selection in IIT-JEE is 45. Ridhima took coaching at FIIT-JEE....the probability that only 1 of them cracks the Exam?

Question 4. Let X be a set containing n elements. If two subsets A and B of X are picked at random, the probability that A and ....probability that A and B the same number of elements, is

Question 5. Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively ....

Question 6. Urn A contains 6 red and 4 black balls and urn B contains 4 red and 6 black balls. One ball is drawn at random from....the probability that it is found to be red, is

Question 7. Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are p....The probability that no two black balls are placed adjacently equals

Question 8. There are four machines and it is known that exactly two of them are faulty. They are tested, one by one, is a rand....identified. Then the probability that only two tests are needed

Question 9. Probability of a fraudster being caught is 12 and committing a fraud is 35. What is his chance of not going to jail?....

Question 10. One of the two events must occur. If the chance of one is 23 of the other, then odds in favour of the other are....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0