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Among a group of 5 boys and 6 girls, 4 members is to be selected for an event. Find the probability that at least one boy is selected ?
- a)17/22
- b)19/22
- c)21/22
- d)15/22
Correct answer is option 'C'. Can you explain this answer?
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Among a group of 5 boys and 6 girls, 4 members is to be selected for a...
we can solve this by calculating the probability of the opposite event (no boys selected) and subtracting it from 1 (since probabilities of all events must sum to 1).
Here's how:
Step 1: Probability of no boys selected (unfavorable event)
- We can choose 4 girls out of 6 girls in ⁶C₄ ways (combinations, order doesn't matter).
- The total number of ways to choose 4 members from 11 (5 boys + 6 girls) is ¹¹C₄ ways.
Probability (no boys) = Favorable cases (girls only) / Total cases = ⁶C₄ / ¹¹C₄
Step 2: Probability of at least one boy (favorable event)
Probability (at least one boy) = 1 - Probability (no boys)
Calculation:
⁶C₄ = (6 * 5 * 4 * 3) / (4 * 3 * 2 * 1) = 15 ¹¹C₄ = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330
Probability (no boys) = 15 / 330 = 1/22
Probability (at least one boy) = 1 - (1/22) = 21/22
Therefore, the probability that at least one boy is selected is 21/22.
Most Upvoted Answer
Among a group of 5 boys and 6 girls, 4 members is to be selected for a...
Given information:
- 5 boys and 6 girls
- need to select 4 members for an event
- find the probability that at least one boy is selected
To find the probability, we need to use the formula:
P(event) = number of favorable outcomes / total number of outcomes
Total number of outcomes:
We need to select 4 members from a group of 11. The total number of ways to do this is:
11C4 = (11!)/(4!7!) = 330
Number of favorable outcomes:
We can calculate the number of favorable outcomes by finding the probability that no boys are selected, and then subtracting this from 1 to get the probability that at least one boy is selected.
No boys are selected:
If no boys are selected, then we need to select 4 girls from a group of 6. The number of ways to do this is:
6C4 = (6!)/(4!2!) = 15
At least one boy is selected:
To get the probability that at least one boy is selected, we can subtract the probability that no boys are selected from 1:
P(at least one boy) = 1 - P(no boys)
P(at least one boy) = 1 - 15/330
P(at least one boy) = 315/330
P(at least one boy) = 21/22
Therefore, the answer is option (c) 21/22.
- 5 boys and 6 girls
- need to select 4 members for an event
- find the probability that at least one boy is selected
To find the probability, we need to use the formula:
P(event) = number of favorable outcomes / total number of outcomes
Total number of outcomes:
We need to select 4 members from a group of 11. The total number of ways to do this is:
11C4 = (11!)/(4!7!) = 330
Number of favorable outcomes:
We can calculate the number of favorable outcomes by finding the probability that no boys are selected, and then subtracting this from 1 to get the probability that at least one boy is selected.
No boys are selected:
If no boys are selected, then we need to select 4 girls from a group of 6. The number of ways to do this is:
6C4 = (6!)/(4!2!) = 15
At least one boy is selected:
To get the probability that at least one boy is selected, we can subtract the probability that no boys are selected from 1:
P(at least one boy) = 1 - P(no boys)
P(at least one boy) = 1 - 15/330
P(at least one boy) = 315/330
P(at least one boy) = 21/22
Therefore, the answer is option (c) 21/22.
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