Question:
A and B throw one dice for a stake of Rs.11, which is to be won by the player who first throws a six. The game ends when the stake is won by A or B. If A has the first throw, what are their respective expectations?
A and B throw one dice for a stake of Rs.11, which is to be won by the player who first throws a six. The game ends when the stake is won by A or B. If A has the first throw, what are their respective expectations?
Show Hint
Since A throws first, his winning chance is 6/11 versus B's 5/11; multiply each by the Rs.11 stake.
Updated On: Jul 14, 2026
- 5 and 6
- 6 and 5
- 11 and 0
- 10 and 1
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: A wins on turn k with probability (5/6)^(2(k-1)) x 1/6.
Summing this geometric series with first term 1/6 and ratio 25/36:
P(A wins) = (1/6) / (1 - 25/36) = (1/6) / (11/36) = 6/11
Step 2: B's probability.
P(B wins) = 1 - 6/11 = 5/11
Step 3: Compute expectations.
E(A) = 6/11 x 11 = 6
E(B) = 5/11 x 11 = 5
Final Answer: A's expectation is Rs.6 and B's expectation is Rs.5.
Summing this geometric series with first term 1/6 and ratio 25/36:
P(A wins) = (1/6) / (1 - 25/36) = (1/6) / (11/36) = 6/11
Step 2: B's probability.
P(B wins) = 1 - 6/11 = 5/11
Step 3: Compute expectations.
E(A) = 6/11 x 11 = 6
E(B) = 5/11 x 11 = 5
Final Answer: A's expectation is Rs.6 and B's expectation is Rs.5.
Was this answer helpful?
0
0
Top SNAP Quantitative Ability and Data Interpretation Questions
- In a retail outlet, the average revenue was Rs.10,000 per day over a 30 day period. During this period, the average revenue on weekends (total 8 days) was Rs. 20,000 per day. What was the average daily revenue on weekdays?
- Two different prime numbers X and Y, both are greater than 2, then which of the following must be true?
- It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B alone takes 8 hours to fill the same tank. A, B and another pump C all together fill the tank in 2 hours. How long would pump C take, used alone, to fill the tank?
- A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am, pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am?
- The sum of prime numbers that are greater than 60, but less than 70 is :
View More Questions
Top SNAP Probability Questions
- A survey was conducted of 100 people whether they have read recent issues of 'Golmal', a monthly magazine. Summarized information is presented below :
Only September: 18
September but not August: 23
September and July: 8
September: 28
July: 48
July and August: 10
None of the three months: 24
What is the number of surveyed people who have read exactly for two consecutive months? - A bag contains 5 white and 3 black balls; another bag contains 4 white and 5 black balls. From any one of these bags a single draw of two balls is made. Find the probability that one of them would be white and another black ball.
- The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays, is:
- There are five boys and three girls who are sitting together to discuss a management problem at a round table. In how many ways can they sit around the table so that no two girls are together ?
- The number of ways in which a committee of 3 ladies and 4 gentlemen can be appointed from a meeting consisting of 8 ladies and 7 gentlemen, if Mrs. X refuses to serve in a committee if Mr. Y is its member, is
View More Questions
Top SNAP Questions
- In a retail outlet, the average revenue was Rs.10,000 per day over a 30 day period. During this period, the average revenue on weekends (total 8 days) was Rs. 20,000 per day. What was the average daily revenue on weekdays?
- Two different prime numbers X and Y, both are greater than 2, then which of the following must be true?
- It takes 6 hours for pump A, used alone, to fill a tank of water. Pump B alone takes 8 hours to fill the same tank. A, B and another pump C all together fill the tank in 2 hours. How long would pump C take, used alone, to fill the tank?
- A swimming pool can be filled by pipe A in 3 hours and by pipe B in 6 hours, each pump working on its own. At 9 am, pump A is started. At what time will the swimming pool be filled if pump B is started at 10 am?
- The sum of prime numbers that are greater than 60, but less than 70 is :
View More Questions