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A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is
- a)1/3
- b)3/7
- c)1/2
- d)4/7
Correct answer is option 'C'. Can you explain this answer?
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A box contains 4 white balls and 3 red balls. In succession, two balls...
After first ball is drawn white then sample space has 4 + 3 – 1 = 6 balls. Probability of second ball is red without replacement
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A box contains 4 white balls and 3 red balls. In succession, two balls...
Problem:
A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is:
a) 1/3
b) 3/7
c) 1/2
d) 4/7
Solution:
To find the probability that the second removed ball is red, given that the first removed ball is white, we can use conditional probability.
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are events.
In this problem, we want to find P(Red ball is selected second|White ball is selected first), which can be written as P(R|W).
Step 1: Find the Probability of Selecting a White Ball First
The probability of selecting a white ball first can be calculated by dividing the number of white balls by the total number of balls:
P(White ball is selected first) = Number of white balls / Total number of balls = 4 / 7
Step 2: Find the Probability of Selecting a Red Ball Second, Given that a White Ball is Selected First
Since we know that a white ball is selected first, the total number of balls is reduced by 1. Therefore, the probability of selecting a red ball second, given that a white ball is selected first, can be calculated by dividing the number of red balls by the reduced total number of balls:
P(Red ball is selected second|White ball is selected first) = Number of red balls / (Total number of balls - 1) = 3 / 6 = 1 / 2
Conclusion:
The probability that the second removed ball is red, given that the first removed ball is white, is 1/2. Therefore, the correct answer is option C.
A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is:
a) 1/3
b) 3/7
c) 1/2
d) 4/7
Solution:
To find the probability that the second removed ball is red, given that the first removed ball is white, we can use conditional probability.
Conditional Probability:
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), where A and B are events.
In this problem, we want to find P(Red ball is selected second|White ball is selected first), which can be written as P(R|W).
Step 1: Find the Probability of Selecting a White Ball First
The probability of selecting a white ball first can be calculated by dividing the number of white balls by the total number of balls:
P(White ball is selected first) = Number of white balls / Total number of balls = 4 / 7
Step 2: Find the Probability of Selecting a Red Ball Second, Given that a White Ball is Selected First
Since we know that a white ball is selected first, the total number of balls is reduced by 1. Therefore, the probability of selecting a red ball second, given that a white ball is selected first, can be calculated by dividing the number of red balls by the reduced total number of balls:
P(Red ball is selected second|White ball is selected first) = Number of red balls / (Total number of balls - 1) = 3 / 6 = 1 / 2
Conclusion:
The probability that the second removed ball is red, given that the first removed ball is white, is 1/2. Therefore, the correct answer is option C.
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A box contains 4 white balls and 3 red balls. In succession, two balls are randomly selected and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red isa)1/3 b)3/7 c)1/2 d)4/7Correct answer is option 'C'. Can you explain this answer?
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