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A box contains 5 block 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)1/2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A box contains 5 block 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)
∴ Probability of getting two black balls and one red ball is 15/28.
(B = Black ball, R = Red balls)
∴ Probability of getting two black balls and one red ball is 15/28.
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Community Answer
A box contains 5 block balls and 3 red balls. A total of three balls a...
To find the probability of getting two black balls and one red ball, we need to consider the different ways in which this can occur and calculate the probability for each case.
Let's break down the problem into steps:
Step 1: Total number of balls
- The box contains 5 black balls and 3 red balls.
- So, the total number of balls in the box is 8.
Step 2: Probability of picking a black ball on the first draw
- Since there are 5 black balls out of 8 total balls, the probability of picking a black ball on the first draw is 5/8.
Step 3: Probability of picking a black ball on the second draw
- After the first ball is drawn, there are now 4 black balls left out of 7 remaining balls.
- So, the probability of picking a black ball on the second draw is 4/7.
Step 4: Probability of picking a red ball on the third draw
- After the second ball is drawn, there are now 3 red balls left out of 6 remaining balls.
- So, the probability of picking a red ball on the third draw is 3/6, which simplifies to 1/2.
Step 5: Combining the probabilities
- To find the probability of all three events happening (picking two black balls and one red ball), we multiply the individual probabilities together.
- So, the probability is (5/8) * (4/7) * (1/2) = 20/112 = 5/28.
Therefore, the probability of getting two black balls and one red ball is 5/28, which corresponds to option C.
Let's break down the problem into steps:
Step 1: Total number of balls
- The box contains 5 black balls and 3 red balls.
- So, the total number of balls in the box is 8.
Step 2: Probability of picking a black ball on the first draw
- Since there are 5 black balls out of 8 total balls, the probability of picking a black ball on the first draw is 5/8.
Step 3: Probability of picking a black ball on the second draw
- After the first ball is drawn, there are now 4 black balls left out of 7 remaining balls.
- So, the probability of picking a black ball on the second draw is 4/7.
Step 4: Probability of picking a red ball on the third draw
- After the second ball is drawn, there are now 3 red balls left out of 6 remaining balls.
- So, the probability of picking a red ball on the third draw is 3/6, which simplifies to 1/2.
Step 5: Combining the probabilities
- To find the probability of all three events happening (picking two black balls and one red ball), we multiply the individual probabilities together.
- So, the probability is (5/8) * (4/7) * (1/2) = 20/112 = 5/28.
Therefore, the probability of getting two black balls and one red ball is 5/28, which corresponds to option C.
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