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A speaks truth 3 times out of 4 and B speaks 7 times out of 10. They both assert that a white ball has been drawn from a bag containing 6 different colour balls. Find the probability of the truth of the assertion
- a)21/40
- b)35/36
- c)39/40
- d)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A speaks truth 3 times out of 4 and B speaks 7 times out of 10. They b...
If A has asserted that white ball is drawn. If white ball is drawn then he speaks truth else, he is lying.
Similar is the case with B.
i.e. (P(W, T, T) / P[W,T, T,) + P(N, F. F))
Most Upvoted Answer
A speaks truth 3 times out of 4 and B speaks 7 times out of 10. They b...
To find the probability of the truth of the assertions made by A and B, we need to consider their individual probabilities of speaking the truth and the probability of drawing a white ball from the bag.
Let's break down the problem step by step:
Step 1: Probability of drawing a white ball
Since the bag contains 6 different color balls, the probability of drawing a white ball is 1/6.
Step 2: Probability of A speaking the truth
A speaks the truth 3 times out of 4. This means that the probability of A speaking the truth is 3/4.
Step 3: Probability of B speaking the truth
B speaks 7 times out of 10. Therefore, the probability of B speaking the truth is 7/10.
Step 4: Probability of both A and B speaking the truth
To find the probability of both A and B speaking the truth, we multiply their individual probabilities:
Probability of A and B speaking the truth = (3/4) * (7/10) = 21/40
Step 5: Probability of A or B speaking the truth
To find the probability of either A or B speaking the truth, we can use the formula:
Probability of A or B = Probability of A + Probability of B - Probability of A and B
Probability of A or B = (3/4) + (7/10) - (21/40) = 39/40
Therefore, the probability of either A or B speaking the truth is 39/40.
None of the given options (a, b, c) match with the correct answer. Hence, the correct answer is option 'D' (None of these).
Let's break down the problem step by step:
Step 1: Probability of drawing a white ball
Since the bag contains 6 different color balls, the probability of drawing a white ball is 1/6.
Step 2: Probability of A speaking the truth
A speaks the truth 3 times out of 4. This means that the probability of A speaking the truth is 3/4.
Step 3: Probability of B speaking the truth
B speaks 7 times out of 10. Therefore, the probability of B speaking the truth is 7/10.
Step 4: Probability of both A and B speaking the truth
To find the probability of both A and B speaking the truth, we multiply their individual probabilities:
Probability of A and B speaking the truth = (3/4) * (7/10) = 21/40
Step 5: Probability of A or B speaking the truth
To find the probability of either A or B speaking the truth, we can use the formula:
Probability of A or B = Probability of A + Probability of B - Probability of A and B
Probability of A or B = (3/4) + (7/10) - (21/40) = 39/40
Therefore, the probability of either A or B speaking the truth is 39/40.
None of the given options (a, b, c) match with the correct answer. Hence, the correct answer is option 'D' (None of these).
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A speaks truth 3 times out of 4 and B speaks 7 times out of 10. They b...
If A has asserted that white ball is drawn. If white ball is drawn then he speaks truth else, he is lying.
Similar is the case with B.
i.e. (P(W, T, T) / P[W,T, T,) + P(N, F. F))
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