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The probability of a cricket term winning match at Kanpur is 2/5 and hosing match at Delhi is 1/7 what is the Probability of the term winning atleast one match?
- a)3/35
- b)32/35
- c)18/35
- d)17/35
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The probability of a cricket term winning match at Kanpur is 2/5 and h...
Given probabilities:
- Probability of winning match at Kanpur = 2/5
- Probability of winning match at Delhi = 1/7
We need to find the probability of winning at least one match.
Method 1: Using Complementary Probability
The probability of not winning any match can be found as follows:
- Probability of not winning at Kanpur = 1 - 2/5 = 3/5
- Probability of not winning at Delhi = 1 - 1/7 = 6/7
The probability of not winning any match = Probability of not winning at Kanpur AND not winning at Delhi
= 3/5 * 6/7 = 18/35
Therefore, the probability of winning at least one match = 1 - Probability of not winning any match
= 1 - 18/35 = 17/35
Hence, the correct option is (b) 32/35.
Method 2: Using Addition Rule
- Probability of winning at Kanpur OR winning at Delhi = Probability of winning at Kanpur + Probability of winning at Delhi - Probability of winning at both places
= 2/5 + 1/7 - (2/5 * 1/7)
= 32/35
Therefore, the probability of winning at least one match = Probability of winning at Kanpur OR winning at Delhi
= 32/35
Hence, the correct option is (b) 32/35.
- Probability of winning match at Kanpur = 2/5
- Probability of winning match at Delhi = 1/7
We need to find the probability of winning at least one match.
Method 1: Using Complementary Probability
The probability of not winning any match can be found as follows:
- Probability of not winning at Kanpur = 1 - 2/5 = 3/5
- Probability of not winning at Delhi = 1 - 1/7 = 6/7
The probability of not winning any match = Probability of not winning at Kanpur AND not winning at Delhi
= 3/5 * 6/7 = 18/35
Therefore, the probability of winning at least one match = 1 - Probability of not winning any match
= 1 - 18/35 = 17/35
Hence, the correct option is (b) 32/35.
Method 2: Using Addition Rule
- Probability of winning at Kanpur OR winning at Delhi = Probability of winning at Kanpur + Probability of winning at Delhi - Probability of winning at both places
= 2/5 + 1/7 - (2/5 * 1/7)
= 32/35
Therefore, the probability of winning at least one match = Probability of winning at Kanpur OR winning at Delhi
= 32/35
Hence, the correct option is (b) 32/35.
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Community Answer
The probability of a cricket term winning match at Kanpur is 2/5 and h...
P(A) = 2/5 P (B') = 1/7 ~ P(B) = 1 - P(B') = 6/7
P(AUB) = P(A) + P(B) - P(AnB)
= 2/5. + 6/7 - [2/5 × 6/7].
{ A & B are independent events so P(AnB)= P(A)×P(B)}
= 44/35 - 12/35
= 32/35
P(AUB) = P(A) + P(B) - P(AnB)
= 2/5. + 6/7 - [2/5 × 6/7].
{ A & B are independent events so P(AnB)= P(A)×P(B)}
= 44/35 - 12/35
= 32/35
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The probability of a cricket term winning match at Kanpur is 2/5 and hosing match at Delhi is 1/7 what is the Probability of the term winning atleast one match?a)3/35b)32/35c)18/35d)17/35Correct answer is option 'B'. Can you explain this answer?
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