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A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is
- a)3/8
- b)2/15
- c)15/28
- d)½
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A box contains 5 black balls and 3 red balls. A total of three balls a...
Here the possible combination of picking up three balls without replacement is BBR, BRB, RBB.
(B = Black ball, R = Red balls)
9
∴ Probability of getting two black balls and one red ball is (5/28)x3 = 15/28.
Most Upvoted Answer
A box contains 5 black balls and 3 red balls. A total of three balls a...
Problem:
A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is
a) 3/8
b) 2/15
c) 15/28
d)
Solution:
To find the probability of getting two black balls and one red ball, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have two black balls and one red ball, we can choose 2 black balls out of the 5 available and one red ball out of the 3 available. The number of ways to do this can be calculated using combinations.
Number of ways to choose 2 black balls from 5: C(5, 2) = 10
Number of ways to choose 1 red ball from 3: C(3, 1) = 3
Therefore, the number of favorable outcomes = 10 * 3 = 30
Total Outcomes:
To calculate the total number of possible outcomes, we need to consider the number of ways to choose 3 balls from the total 8 balls in the box.
Number of ways to choose 3 balls from 8: C(8, 3) = 56
Therefore, the total number of possible outcomes = 56
Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability of getting two black balls and one red ball = Favorable outcomes / Total outcomes = 30 / 56 = 15 / 28
Therefore, the correct answer is option c) 15/28.
A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is
a) 3/8
b) 2/15
c) 15/28
d)
Solution:
To find the probability of getting two black balls and one red ball, we need to consider the number of favorable outcomes and the total number of possible outcomes.
Favorable Outcomes:
To have two black balls and one red ball, we can choose 2 black balls out of the 5 available and one red ball out of the 3 available. The number of ways to do this can be calculated using combinations.
Number of ways to choose 2 black balls from 5: C(5, 2) = 10
Number of ways to choose 1 red ball from 3: C(3, 1) = 3
Therefore, the number of favorable outcomes = 10 * 3 = 30
Total Outcomes:
To calculate the total number of possible outcomes, we need to consider the number of ways to choose 3 balls from the total 8 balls in the box.
Number of ways to choose 3 balls from 8: C(8, 3) = 56
Therefore, the total number of possible outcomes = 56
Probability:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of possible outcomes.
Probability of getting two black balls and one red ball = Favorable outcomes / Total outcomes = 30 / 56 = 15 / 28
Therefore, the correct answer is option c) 15/28.
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A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is a)3/8 b)2/15 c)15/28 d)½Correct answer is option 'C'. Can you explain this answer?
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