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A bag contains 5 red balls, 6 yellow and 3 green balls. If two balls are picked at random, what is the probability that both are red or both are green in colour?
- a)3/7
- b)5/14
- c)1/7
- d)2/7
- e)3/14
Correct answer is option 'C'. Can you explain this answer?
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Problem:
A bag contains 5 red balls, 6 yellow balls, and 3 green balls. If two balls are picked at random, what is the probability that both are red or both are green in color?
Solution:
To solve this problem, we need to find the probability of selecting two red balls or two green balls from the bag.
Step 1: Find the total number of ways to select 2 balls from the bag:
The total number of balls in the bag is 5 + 6 + 3 = 14.
Therefore, the total number of ways to select 2 balls from the bag is given by the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 14 and r = 2.
So, the total number of ways to select 2 balls from the bag is:
14C2 = 14! / (2!(14-2)!) = 91
Step 2: Find the number of ways to select 2 red balls:
There are 5 red balls in the bag.
So, the number of ways to select 2 red balls is given by the combination formula:
5C2 = 5! / (2!(5-2)!) = 10
Step 3: Find the number of ways to select 2 green balls:
There are 3 green balls in the bag.
So, the number of ways to select 2 green balls is given by the combination formula:
3C2 = 3! / (2!(3-2)!) = 3
Step 4: Find the probability of selecting two red balls or two green balls:
The probability of an event is given by the formula:
P(event) = number of favorable outcomes / total number of possible outcomes
In this case, the number of favorable outcomes is 10 (selecting 2 red balls) + 3 (selecting 2 green balls) = 13.
Therefore, the probability of selecting two red balls or two green balls is:
P(both red or both green) = 13 / 91 = 1/7
Hence, the correct answer is option 'C' (1/7).
A bag contains 5 red balls, 6 yellow balls, and 3 green balls. If two balls are picked at random, what is the probability that both are red or both are green in color?
Solution:
To solve this problem, we need to find the probability of selecting two red balls or two green balls from the bag.
Step 1: Find the total number of ways to select 2 balls from the bag:
The total number of balls in the bag is 5 + 6 + 3 = 14.
Therefore, the total number of ways to select 2 balls from the bag is given by the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, n = 14 and r = 2.
So, the total number of ways to select 2 balls from the bag is:
14C2 = 14! / (2!(14-2)!) = 91
Step 2: Find the number of ways to select 2 red balls:
There are 5 red balls in the bag.
So, the number of ways to select 2 red balls is given by the combination formula:
5C2 = 5! / (2!(5-2)!) = 10
Step 3: Find the number of ways to select 2 green balls:
There are 3 green balls in the bag.
So, the number of ways to select 2 green balls is given by the combination formula:
3C2 = 3! / (2!(3-2)!) = 3
Step 4: Find the probability of selecting two red balls or two green balls:
The probability of an event is given by the formula:
P(event) = number of favorable outcomes / total number of possible outcomes
In this case, the number of favorable outcomes is 10 (selecting 2 red balls) + 3 (selecting 2 green balls) = 13.
Therefore, the probability of selecting two red balls or two green balls is:
P(both red or both green) = 13 / 91 = 1/7
Hence, the correct answer is option 'C' (1/7).
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A bag contains 5 red balls, 6 yellow and 3 green balls. If two balls are picked at random, what is the probability that both are red or both are green in colour?a)3/7b)5/14c)1/7d)2/7e)3/14Correct answer is option 'C'. Can you explain this answer?
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