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A bag contains 4 white, 8 black and 6 blue balls. If two balls are drawn at random, find the probability of both the balls being black?
- a)22/137
- b)14/123
- c)28/253
- d)7/105
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A bag contains 4 white, 8 black and 6 blue balls. If two balls are dra...
n(S) = 18C2 = 153
There are eight black balls, out of which two balls are drawn in 8C2 ways.
n(E) = 28
P(E) = 28 /153 = 28/153
There are eight black balls, out of which two balls are drawn in 8C2 ways.
n(E) = 28
P(E) = 28 /153 = 28/153
Most Upvoted Answer
A bag contains 4 white, 8 black and 6 blue balls. If two balls are dra...
To find the probability of drawing two black balls from the bag, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of balls in the bag = 4 white + 8 black + 6 blue = 18
Total number of possible outcomes when drawing two balls = selecting 2 balls out of 18 = 18C2 = (18!)/(2!(18-2)!) = (18*17)/(2*1) = 153
The number of favorable outcomes is the number of ways we can select 2 black balls from the 8 black balls. We can calculate this using combinations:
Number of ways to select 2 black balls = 8C2 = (8!)/(2!(8-2)!) = (8*7)/(2*1) = 28
Now we can calculate the probability of drawing two black balls by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 28/153
Probability = 28/153 = 0.183
Therefore, the probability of drawing two black balls from the bag is 28/153 or approximately 0.183. The correct answer is option C, 28/253.
Total number of balls in the bag = 4 white + 8 black + 6 blue = 18
Total number of possible outcomes when drawing two balls = selecting 2 balls out of 18 = 18C2 = (18!)/(2!(18-2)!) = (18*17)/(2*1) = 153
The number of favorable outcomes is the number of ways we can select 2 black balls from the 8 black balls. We can calculate this using combinations:
Number of ways to select 2 black balls = 8C2 = (8!)/(2!(8-2)!) = (8*7)/(2*1) = 28
Now we can calculate the probability of drawing two black balls by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 28/153
Probability = 28/153 = 0.183
Therefore, the probability of drawing two black balls from the bag is 28/153 or approximately 0.183. The correct answer is option C, 28/253.
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