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Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of at least one of the events E and F is:
- a)1/50
- b)1/25
- c)13/50
- d)49/50
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Suppose E and F are two events of a random experiment. If the probabil...
Given Information:
- Probability of occurrence of E = 1/5
- Probability of occurrence of F given E = 1/10
To Find:
Probability of non-occurrence of at least one of the events E and F
Solution:
1. Probability of occurrence of both E and F = P(E) * P(F|E)
= (1/5) * (1/10)
= 1/50
2. Probability of occurrence of at least one of the events E and F = P(E union F)
= P(E) + P(F) - P(E intersect F)
(where P(E intersect F) = P(E) * P(F|E) as given in the question)
= P(E) + P(F|E) - P(E) * P(F|E)
= (1/5) + (1/10) - (1/50)
= 9/50
3. Probability of non-occurrence of at least one of the events E and F = 1 - P(E union F)
= 1 - (9/50)
= 41/50
= 49/50 (after simplification)
Therefore, the probability of non-occurrence of at least one of the events E and F is 49/50.
Answer: (d) 49/50
- Probability of occurrence of E = 1/5
- Probability of occurrence of F given E = 1/10
To Find:
Probability of non-occurrence of at least one of the events E and F
Solution:
1. Probability of occurrence of both E and F = P(E) * P(F|E)
= (1/5) * (1/10)
= 1/50
2. Probability of occurrence of at least one of the events E and F = P(E union F)
= P(E) + P(F) - P(E intersect F)
(where P(E intersect F) = P(E) * P(F|E) as given in the question)
= P(E) + P(F|E) - P(E) * P(F|E)
= (1/5) + (1/10) - (1/50)
= 9/50
3. Probability of non-occurrence of at least one of the events E and F = 1 - P(E union F)
= 1 - (9/50)
= 41/50
= 49/50 (after simplification)
Therefore, the probability of non-occurrence of at least one of the events E and F is 49/50.
Answer: (d) 49/50
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Suppose E and F are two events of a random experiment. If the probabil...
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Suppose E and F are two events of a random experiment. If the probability of occurrence of E is 1/5 and the probability of occurrence of F given E is 1/10, then the probability of non-occurrence of at least one of the events E and F is:a)1/50b)1/25c)13/50d)49/50Correct answer is option 'D'. Can you explain this answer?
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