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An urn contain 6 orange, 4 green,3 pink and 4 black balls
Q.
If 5 balls are picked at random, what is the probability that none are orange ?
- a)33/442
- b)442/33
- c)15/167
- d)23/235
Correct answer is option 'A'. 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 5 balls...
17C5 = 17*16*15*14*13/5*4*3*2*1 = 742560/120 = 6188
11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462
P = 462/6188 = 33/442
11C5 = 11*10*9*8*7/5*4*3*2*1 = 55440/120 = 462
P = 462/6188 = 33/442
Most Upvoted Answer
An urn contain 6 orange, 4 green,3 pink and 4 black ballsQ. If 5 balls...
Problem:
An urn contains 6 orange, 4 green, 3 pink, and 4 black balls. If 5 balls are picked at random, what is the probability that none are orange?
Solution:
To find the probability that none of the chosen balls are orange, we need to calculate the number of favorable outcomes (picking 5 balls without any orange) divided by the total number of possible outcomes (picking any 5 balls).
Step 1: Find the total number of possible outcomes:
To find the total number of possible outcomes, we need to calculate the number of ways to choose 5 balls out of the total number of balls in the urn.
Total number of balls in the urn = 6 orange + 4 green + 3 pink + 4 black = 17 balls
So, the total number of possible outcomes = C(17, 5) = 17! / (5! * (17-5)!) = 6188
Step 2: Find the number of favorable outcomes:
To find the number of favorable outcomes, we need to calculate the number of ways to choose 5 balls without any orange.
Number of ways to choose 5 balls without any orange = C(11, 5) = 11! / (5! * (11-5)!) = 462
Step 3: Calculate the probability:
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 462 / 6188
Probability = 33 / 442
Therefore, the probability that none of the 5 balls chosen are orange is 33 / 442.
So, the correct answer is option 'A' (33/442).
An urn contains 6 orange, 4 green, 3 pink, and 4 black balls. If 5 balls are picked at random, what is the probability that none are orange?
Solution:
To find the probability that none of the chosen balls are orange, we need to calculate the number of favorable outcomes (picking 5 balls without any orange) divided by the total number of possible outcomes (picking any 5 balls).
Step 1: Find the total number of possible outcomes:
To find the total number of possible outcomes, we need to calculate the number of ways to choose 5 balls out of the total number of balls in the urn.
Total number of balls in the urn = 6 orange + 4 green + 3 pink + 4 black = 17 balls
So, the total number of possible outcomes = C(17, 5) = 17! / (5! * (17-5)!) = 6188
Step 2: Find the number of favorable outcomes:
To find the number of favorable outcomes, we need to calculate the number of ways to choose 5 balls without any orange.
Number of ways to choose 5 balls without any orange = C(11, 5) = 11! / (5! * (11-5)!) = 462
Step 3: Calculate the probability:
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 462 / 6188
Probability = 33 / 442
Therefore, the probability that none of the 5 balls chosen are orange is 33 / 442.
So, the correct answer is option 'A' (33/442).
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