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A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game is
- a)3/7
- b)9/41
- c)4/7
- d)9/11
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
A and B take turn in throwing a pair of dice. A wins if he throws a to...
Solution:
Let's use probability tree diagram to solve this problem.
Probability tree diagram:
A has the first throw, if the sum of the numbers on the dice is 5, A wins. If the sum of the numbers on the dice is anything other than 5, the turn goes to B.
If B gets a sum of 7 before A gets 5, B wins. If B gets anything other than 7, the turn goes back to A.
Calculation:
Let's calculate the probability of A winning the game.
P(A wins on the first throw) = 4/36 = 1/9
(There are 4 ways to get a sum of 5 on a pair of dice out of the 36 possible outcomes)
P(A wins on the second throw) = (20/36)(10/36) = 50/1296
(A gets anything other than 5 on the first throw with probability 5/9. B gets anything other than 7 on the first throw with probability 25/36. So, the probability of A winning on the second throw is (5/9)(25/36)(4/36) = 50/1296)
P(A wins on the third throw) = (20/36)(26/36)(20/36)(10/36) = 250/5832
(A gets anything other than 5 on the first two throws with probability (5/9)(20/36). B gets anything other than 7 on the first two throws with probability (25/36)(26/36). A wins on the third throw with probability (5/9)(20/36)(25/36)(4/36) = 250/5832)
P(A wins on the fourth throw) = (20/36)(26/36)(20/36)(26/36)(20/36)(10/36) = 1250/139968
(The probability of A winning on the fourth throw is (5/9)(20/36)(25/36)(20/36)(25/36)(4/36) = 1250/139968)
P(A wins) = 1/9 + 50/1296 + 250/5832 + 1250/139968 = 3/7
Therefore, the probability of A winning the game is 3/7, which is option A.
Let's use probability tree diagram to solve this problem.
Probability tree diagram:
A has the first throw, if the sum of the numbers on the dice is 5, A wins. If the sum of the numbers on the dice is anything other than 5, the turn goes to B.
If B gets a sum of 7 before A gets 5, B wins. If B gets anything other than 7, the turn goes back to A.
Calculation:
Let's calculate the probability of A winning the game.
P(A wins on the first throw) = 4/36 = 1/9
(There are 4 ways to get a sum of 5 on a pair of dice out of the 36 possible outcomes)
P(A wins on the second throw) = (20/36)(10/36) = 50/1296
(A gets anything other than 5 on the first throw with probability 5/9. B gets anything other than 7 on the first throw with probability 25/36. So, the probability of A winning on the second throw is (5/9)(25/36)(4/36) = 50/1296)
P(A wins on the third throw) = (20/36)(26/36)(20/36)(10/36) = 250/5832
(A gets anything other than 5 on the first two throws with probability (5/9)(20/36). B gets anything other than 7 on the first two throws with probability (25/36)(26/36). A wins on the third throw with probability (5/9)(20/36)(25/36)(4/36) = 250/5832)
P(A wins on the fourth throw) = (20/36)(26/36)(20/36)(26/36)(20/36)(10/36) = 1250/139968
(The probability of A winning on the fourth throw is (5/9)(20/36)(25/36)(20/36)(25/36)(4/36) = 1250/139968)
P(A wins) = 1/9 + 50/1296 + 250/5832 + 1250/139968 = 3/7
Therefore, the probability of A winning the game is 3/7, which is option A.
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A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer?
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A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer?.
A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A and B take turn in throwing a pair of dice. A wins if he throws a total of 5 before B throws a total of 7. If A has the first throw, the probability of his winning the game isa)3/7b)9/41c)4/7d)9/11Correct answer is option 'A'. Can you explain this answer?.
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