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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red is
- a)1/90
- b)1/2
- c)19/90
- d)2/9
Correct answer is option 'D'. Can you explain this answer?
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A box contains 5 black and 5 red balls. Two balls are randomly picked ...
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A box contains 5 black and 5 red balls. Two balls are randomly picked ...
Problem:
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. Find the probability for both balls being red.
Solution:
To find the probability of both balls being red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When two balls are drawn one after another without replacement, the total number of outcomes can be calculated by multiplying the number of ways the first ball can be picked with the number of ways the second ball can be picked.
The number of ways the first ball can be picked is 10 (since there are 10 balls in total).
The number of ways the second ball can be picked is 9 (since there is 1 less ball in the box after the first ball is picked).
Therefore, the total number of outcomes is 10 * 9 = 90.
Number of Favorable Outcomes:
To calculate the number of favorable outcomes (i.e., both balls being red), we need to consider that there are initially 5 red balls in the box and that one red ball is removed after the first pick.
The number of ways the first red ball can be picked is 5.
After the first red ball is picked, there are 4 red balls remaining in the box.
Therefore, the number of ways the second red ball can be picked is 4.
Hence, the number of favorable outcomes is 5 * 4 = 20.
Calculating the Probability:
The probability is defined as the number of favorable outcomes divided by the total number of outcomes.
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 20 / 90
Probability = 2 / 9
Thus, the probability for both balls being red is 2/9, which corresponds to option 'D'.
A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. Find the probability for both balls being red.
Solution:
To find the probability of both balls being red, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total Number of Outcomes:
When two balls are drawn one after another without replacement, the total number of outcomes can be calculated by multiplying the number of ways the first ball can be picked with the number of ways the second ball can be picked.
The number of ways the first ball can be picked is 10 (since there are 10 balls in total).
The number of ways the second ball can be picked is 9 (since there is 1 less ball in the box after the first ball is picked).
Therefore, the total number of outcomes is 10 * 9 = 90.
Number of Favorable Outcomes:
To calculate the number of favorable outcomes (i.e., both balls being red), we need to consider that there are initially 5 red balls in the box and that one red ball is removed after the first pick.
The number of ways the first red ball can be picked is 5.
After the first red ball is picked, there are 4 red balls remaining in the box.
Therefore, the number of ways the second red ball can be picked is 4.
Hence, the number of favorable outcomes is 5 * 4 = 20.
Calculating the Probability:
The probability is defined as the number of favorable outcomes divided by the total number of outcomes.
Probability = Number of Favorable Outcomes / Total Number of Outcomes
Probability = 20 / 90
Probability = 2 / 9
Thus, the probability for both balls being red is 2/9, which corresponds to option 'D'.
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A box contains 5 black and 5 red balls. Two balls are randomly picked one after another from the box, without replacement. The probability for both balls being red isa)1/90b)1/2c)19/90d)2/9Correct answer is option 'D'. Can you explain this answer?
Question Description
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