A bag contains 6 red balls and 5 black balls,2 balls are picked,one after the other,find the probability that both are black
The probability that both balls are black is 5/11.
To find the probability of picking two black balls, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes: When two balls are picked one after the other from the bag, there are a total of 11 balls in the bag. So, for the first pick, there are 11 possible balls to choose from. After the first ball is picked, there are only 10 balls left for the second pick.
Total outcomes = 11 * 10 = 110
Number of favorable outcomes: We want to select two black balls. After the first black ball is picked, there are 4 black balls left in the bag. For the second pick, there are only 3 black balls left.
Favorable outcomes = 5 * 4 = 20
Now, we can calculate the probability:
Probability = Favorable outcomes / Total outcomes
= 20 / 110
= 2 / 11
Therefore, the probability of picking two black balls, one after the other, is 2/11.
To find the probability that both balls picked are black, we can use the concept of conditional probability.
Step 1: Determine the probability of picking a black ball on the first draw.
Since there are 11 balls in total (6 red and 5 black), the probability of picking a black ball on the first draw is 5/11.
Step 2: Determine the probability of picking a black ball on the second draw given that the first ball was black.
After the first ball is picked, there are now 10 balls in total with 4 black balls remaining. Therefore, the probability of picking a black ball on the second draw, given that the first ball was black, is 4/10.
Step 3: Multiply the probabilities together.
Since the events of picking a black ball on the first draw and picking a black ball on the second draw are independent, we can multiply the probabilities together:
(5/11) * (4/10) = 20/110 = 2/11
Therefore, the probability that both balls picked are black is 2/11.