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A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw, what is the expectation of his winning the stake?
- a)5/11
- b)15/26
- c)6/11
- d)16/26
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A and B throw with one die for a stake of Rs 11 which is to be won by ...
Probability of obtaining 6 in a single throw is 1/6. Probability that A wins the stake if he get 6 in first throw or if he loses then B also lose and then he get 6 in his second throw i.e. overal 3rd throw and so on.
[sum of infinite terms of G.P.]
[sum of infinite terms of G.P.]Most Upvoted Answer
A and B throw with one die for a stake of Rs 11 which is to be won by ...
Probability of obtaining 6 in a single throw is 1/6. Probability that A wins the stake if he get 6 in first throw or if he loses then B also lose and then he get 6 in his second throw i.e. overal 3rd throw and so on.
[sum of infinite terms of G.P.]
[sum of infinite terms of G.P.]Free Test
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A and B throw with one die for a stake of Rs 11 which is to be won by ...
Given:
A and B are playing a game where they throw a die for a stake of Rs 11. The player who first throws a 6 wins the stake. A has the first throw.
To find:
The expectation of A winning the stake.
Solution:
Step 1: Determine the probability of A winning on the first throw.
- The probability of A throwing a 6 on the first throw is 1/6, as there is only one favorable outcome (getting a 6) out of the six possible outcomes of throwing a die.
Step 2: Determine the probability of A winning on the second throw.
- If A does not win on the first throw, the game moves to B.
- The probability of B not winning on the first throw is 5/6, as there are five possible outcomes (1, 2, 3, 4, 5) out of six which are not favorable for B winning.
- If B does not win on the first throw, the game moves back to A.
- The probability of A winning on the second throw is the same as the probability of A winning on the first throw, which is 1/6.
Step 3: Determine the probability of A winning on the third throw.
- If A does not win on the second throw, the game moves to B.
- The probability of B not winning on the second throw is 5/6.
- If B does not win on the second throw, the game moves back to A.
- The probability of A winning on the third throw is the same as the probability of A winning on the first throw, which is 1/6.
Step 4: Determine the probability of A winning on the nth throw.
- Following the same pattern, the probability of A winning on the nth throw is (1/6)^n.
Step 5: Calculate the expectation of A winning the stake.
- The expectation (E) of A winning the stake is given by the formula:
E = (probability of A winning on the first throw) + (probability of A winning on the second throw) + (probability of A winning on the third throw) + ...
- Plugging in the values, we get:
E = (1/6) + (1/6)^2 + (1/6)^3 + ...
Step 6: Simplify the expectation.
- The expectation can be simplified using the formula for the sum of an infinite geometric series:
E = a / (1 - r)
- In this case, a = 1/6 (the first term) and r = 1/6 (the common ratio).
E = (1/6) / (1 - 1/6)
= (1/6) / (5/6)
= 1/5
Step 7: Simplify the expectation to obtain the final answer.
- The stake is Rs 11, and the probability of A winning the stake is 1/5.
- The expected value of A winning the stake is given by:
Expected value = (probability of A winning) * (stake)
= (1/5) * (11)
=
A and B are playing a game where they throw a die for a stake of Rs 11. The player who first throws a 6 wins the stake. A has the first throw.
To find:
The expectation of A winning the stake.
Solution:
Step 1: Determine the probability of A winning on the first throw.
- The probability of A throwing a 6 on the first throw is 1/6, as there is only one favorable outcome (getting a 6) out of the six possible outcomes of throwing a die.
Step 2: Determine the probability of A winning on the second throw.
- If A does not win on the first throw, the game moves to B.
- The probability of B not winning on the first throw is 5/6, as there are five possible outcomes (1, 2, 3, 4, 5) out of six which are not favorable for B winning.
- If B does not win on the first throw, the game moves back to A.
- The probability of A winning on the second throw is the same as the probability of A winning on the first throw, which is 1/6.
Step 3: Determine the probability of A winning on the third throw.
- If A does not win on the second throw, the game moves to B.
- The probability of B not winning on the second throw is 5/6.
- If B does not win on the second throw, the game moves back to A.
- The probability of A winning on the third throw is the same as the probability of A winning on the first throw, which is 1/6.
Step 4: Determine the probability of A winning on the nth throw.
- Following the same pattern, the probability of A winning on the nth throw is (1/6)^n.
Step 5: Calculate the expectation of A winning the stake.
- The expectation (E) of A winning the stake is given by the formula:
E = (probability of A winning on the first throw) + (probability of A winning on the second throw) + (probability of A winning on the third throw) + ...
- Plugging in the values, we get:
E = (1/6) + (1/6)^2 + (1/6)^3 + ...
Step 6: Simplify the expectation.
- The expectation can be simplified using the formula for the sum of an infinite geometric series:
E = a / (1 - r)
- In this case, a = 1/6 (the first term) and r = 1/6 (the common ratio).
E = (1/6) / (1 - 1/6)
= (1/6) / (5/6)
= 1/5
Step 7: Simplify the expectation to obtain the final answer.
- The stake is Rs 11, and the probability of A winning the stake is 1/5.
- The expected value of A winning the stake is given by:
Expected value = (probability of A winning) * (stake)
= (1/5) * (11)
=
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A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer?
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A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer?.
A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? for Mathematics 2024 is part of Mathematics preparation. The Question and answers have been prepared according to the Mathematics exam syllabus. Information about A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer?.
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A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer?, a detailed solution for A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of A and B throw with one die for a stake of Rs 11 which is to be won by the player who first throws 6. If A has the first throw,what is the expectation of his winning the stake?a)5/11b)15/26c)6/11d)16/26Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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