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Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is :
- a)1/21
- b)2/15
- c)2/21
- d)2/35
Correct answer is option 'C'. Can you explain this answer?
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Two balls are drawn at random from a bag containing 6 white, 4 red and...
To find the probability that both balls drawn are black, we need to determine the total number of ways to draw two balls from the bag and the number of ways to draw two black balls.
Total number of ways to draw two balls:
We have a total of 6 white, 4 red, and 5 black balls in the bag. Therefore, the total number of balls in the bag is 6 + 4 + 5 = 15.
To draw two balls from the bag, we use the combination formula. The number of ways to choose 2 balls out of 15 is given by C(15, 2) = 15! / (2! * (15 - 2)!) = 15! / (2! * 13!) = (15 * 14) / (2 * 1) = 105.
Number of ways to draw two black balls:
We have 5 black balls in the bag. To draw 2 black balls, we use the combination formula. The number of ways to choose 2 black balls out of 5 is given by C(5, 2) = 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Probability of drawing two black balls:
The probability of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcome is drawing two black balls, and the total number of possible outcomes is drawing two balls from the bag.
Therefore, the probability of drawing two black balls is given by:
P(both black) = Number of ways to draw two black balls / Total number of ways to draw two balls
P(both black) = 10 / 105
P(both black) = 2/21
Hence, the correct answer is option 'C' - 2/21.
Total number of ways to draw two balls:
We have a total of 6 white, 4 red, and 5 black balls in the bag. Therefore, the total number of balls in the bag is 6 + 4 + 5 = 15.
To draw two balls from the bag, we use the combination formula. The number of ways to choose 2 balls out of 15 is given by C(15, 2) = 15! / (2! * (15 - 2)!) = 15! / (2! * 13!) = (15 * 14) / (2 * 1) = 105.
Number of ways to draw two black balls:
We have 5 black balls in the bag. To draw 2 black balls, we use the combination formula. The number of ways to choose 2 black balls out of 5 is given by C(5, 2) = 5! / (2! * (5 - 2)!) = 5! / (2! * 3!) = (5 * 4) / (2 * 1) = 10.
Probability of drawing two black balls:
The probability of an event happening is given by the ratio of the number of favorable outcomes to the total number of possible outcomes. In this case, the favorable outcome is drawing two black balls, and the total number of possible outcomes is drawing two balls from the bag.
Therefore, the probability of drawing two black balls is given by:
P(both black) = Number of ways to draw two black balls / Total number of ways to draw two balls
P(both black) = 10 / 105
P(both black) = 2/21
Hence, the correct answer is option 'C' - 2/21.
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Two balls are drawn at random from a bag containing 6 white, 4 red and 5 black balls. The probability that both these balls are black, is :a)1/21b)2/15c)2/21d)2/35Correct answer is option 'C'. Can you explain this answer?
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