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The probabilities that a student will solve Question A and Question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?
- a)0.6
- b)0.7
- c)0.8
- d)0.9
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The probabilities that a student will solve Question A and Question B ...
P = (A ∪ B) = 1 − P(A′ ∩ B′)
= 1 − [(1 − 0.4) × (1 − 0.5)]
= 1 − 0.3 = 0.7
= 1 − [(1 − 0.4) × (1 − 0.5)]
= 1 − 0.3 = 0.7
Most Upvoted Answer
The probabilities that a student will solve Question A and Question B ...
Probability of solving at least one question:
To find the probability that the student solves at least one of the two questions, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given probabilities:
- P(A) = 0.4
- P(B) = 0.5
Calculating the probability of solving both questions:
- P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2
Calculating the probability of solving at least one question:
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A or B) = 0.4 + 0.5 - 0.2
- P(A or B) = 0.9 - 0.2
- P(A or B) = 0.7
Therefore, the probability that the student solves at least one of the two questions is 0.7, which corresponds to option B.
To find the probability that the student solves at least one of the two questions, we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
Given probabilities:
- P(A) = 0.4
- P(B) = 0.5
Calculating the probability of solving both questions:
- P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2
Calculating the probability of solving at least one question:
- P(A or B) = P(A) + P(B) - P(A and B)
- P(A or B) = 0.4 + 0.5 - 0.2
- P(A or B) = 0.9 - 0.2
- P(A or B) = 0.7
Therefore, the probability that the student solves at least one of the two questions is 0.7, which corresponds to option B.
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