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A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ___________.
- a)3/16
- b)45/236
- c)3/4
- d)1/4
Correct answer is option 'B'. Can you explain this answer?
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A box contains 15 blue balls and 45 black balls. If 2 balls are select...
Problem: A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball is _________.
Solution:
To find the probability of the desired outcome, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When selecting 2 balls without replacement, the total number of outcomes can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of balls and r is the number of balls to be selected.
In this case, there are a total of 60 balls (15 blue + 45 black) and we need to select 2 balls. Therefore,
Total number of outcomes = 60C2 = 60! / (2!(60-2)!) = 60! / (2!58!) = (60 * 59) / (2 * 1) = 1770
Number of Favorable Outcomes:
To have a favorable outcome, we need to select a blue ball as the first selection and a black ball as the second selection.
Number of ways to select a blue ball = 15 (since there are 15 blue balls in the box)
After selecting a blue ball, the number of ways to select a black ball = 45 (since there are 45 black balls remaining in the box)
Therefore, the number of favorable outcomes = 15 * 45 = 675
Probability of the Desired Outcome:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 675 / 1770 = 45 / 118
Therefore, the probability of an outcome in which the first selected ball is blue and the second selected ball is black is 45/118.
Hence, the correct answer is option B) 45/236.
Solution:
To find the probability of the desired outcome, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When selecting 2 balls without replacement, the total number of outcomes can be calculated using the combination formula:
nCr = n! / (r!(n-r)!)
where n is the total number of balls and r is the number of balls to be selected.
In this case, there are a total of 60 balls (15 blue + 45 black) and we need to select 2 balls. Therefore,
Total number of outcomes = 60C2 = 60! / (2!(60-2)!) = 60! / (2!58!) = (60 * 59) / (2 * 1) = 1770
Number of Favorable Outcomes:
To have a favorable outcome, we need to select a blue ball as the first selection and a black ball as the second selection.
Number of ways to select a blue ball = 15 (since there are 15 blue balls in the box)
After selecting a blue ball, the number of ways to select a black ball = 45 (since there are 45 black balls remaining in the box)
Therefore, the number of favorable outcomes = 15 * 45 = 675
Probability of the Desired Outcome:
The probability of an event is given by the ratio of the number of favorable outcomes to the total number of outcomes.
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 675 / 1770 = 45 / 118
Therefore, the probability of an outcome in which the first selected ball is blue and the second selected ball is black is 45/118.
Hence, the correct answer is option B) 45/236.
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Community Answer
A box contains 15 blue balls and 45 black balls. If 2 balls are select...
Given : Blue ball = 15, black ball = 45
Total ball = 60
Probability that the outcome in which the first selected is a blue ball and the second selected is a black ball
Hence, the correct option is (B).
Total ball = 60
Probability that the outcome in which the first selected is a blue ball and the second selected is a black ball
Hence, the correct option is (B).
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A box contains 15 blue balls and 45 black balls. If 2 balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is ___________. a)3/16 b)45/236 c)3/4 d)1/4 Correct answer is option 'B'. Can you explain this answer?
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