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An urn contain 6 orange, 4 green,3 pink and 4 black balls
Q.
If 3 balls are picked at random, what is the probability that all are pink ?
- a)2/650
- b)1/680
- c)4/630
- d)3/680
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
An urn contain 6 orange, 4 green,3 pink and 4 black ballsQ. If 3 balls...
17C3 = 17*16*15/3*2*1 = 4080/6 = 680
3C3 = 1
P = 1/680
3C3 = 1
P = 1/680
Most Upvoted Answer
An urn contain 6 orange, 4 green,3 pink and 4 black ballsQ. If 3 balls...
Given:
- Total number of balls in the urn = 6 (orange) + 4 (green) + 3 (pink) + 4 (black) = 17
To find:
- Probability of picking all pink balls when 3 balls are chosen at random
Solution:
To find the probability of picking all pink balls, we need to find the number of favorable outcomes (i.e., picking all pink balls) and the total number of possible outcomes.
Step 1: Finding the number of favorable outcomes:
Since we need to pick all pink balls, we can only choose from the 3 pink balls available in the urn.
Therefore, the number of ways to choose 3 pink balls from the 3 available is given by:
C(3,3) = 1 (where C(n,r) represents the number of combinations of n items taken r at a time)
Step 2: Finding the total number of possible outcomes:
The total number of ways to choose any 3 balls from the 17 balls in the urn is given by:
C(17,3) = (17!)/(3!(17-3)!) = 680
Step 3: Calculating the probability:
The probability of picking all pink balls is given by:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes)
Probability = 1/680
Therefore, the correct answer is option B) 1/680.
- Total number of balls in the urn = 6 (orange) + 4 (green) + 3 (pink) + 4 (black) = 17
To find:
- Probability of picking all pink balls when 3 balls are chosen at random
Solution:
To find the probability of picking all pink balls, we need to find the number of favorable outcomes (i.e., picking all pink balls) and the total number of possible outcomes.
Step 1: Finding the number of favorable outcomes:
Since we need to pick all pink balls, we can only choose from the 3 pink balls available in the urn.
Therefore, the number of ways to choose 3 pink balls from the 3 available is given by:
C(3,3) = 1 (where C(n,r) represents the number of combinations of n items taken r at a time)
Step 2: Finding the total number of possible outcomes:
The total number of ways to choose any 3 balls from the 17 balls in the urn is given by:
C(17,3) = (17!)/(3!(17-3)!) = 680
Step 3: Calculating the probability:
The probability of picking all pink balls is given by:
Probability = (Number of favorable outcomes)/(Total number of possible outcomes)
Probability = 1/680
Therefore, the correct answer is option B) 1/680.
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