a bag contains 3 red, 6 white and 7 blue balls. What is the probility that two balls drawn are white and blue?
To find the probability of drawing two balls that are both white and blue, we need to determine the total number of possible outcomes and the number of favorable outcomes.
1. Total number of possible outcomes:
The bag contains a total of 3 red, 6 white, and 7 blue balls, giving us a total of 16 balls. When we draw two balls without replacement, the total number of possible outcomes is given by the combination formula nCr:
nCr = n! / (r!(n-r)!),
where n is the total number of objects (balls) and r is the number of objects (balls) we want to choose without replacement.
In our case, n = 16 (total number of balls) and r = 2 (balls to be drawn).
The number of total outcomes = 16C2 = 16! / (2!(16-2)!) = (16 * 15) / (2 * 1) = 120.
2. Number of favorable outcomes (white and blue balls):
We want to draw two balls, one white and one blue. We can do this in two ways: drawing a white ball first and then a blue ball, or drawing a blue ball first and then a white ball.
Number of favorable outcomes = Number of ways to draw a white ball and then a blue ball + Number of ways to draw a blue ball and then a white ball.
Number of ways to draw a white ball and then a blue ball:
We have 6 white balls, so the first ball can be any of the 6 white balls, and then we have 7 blue balls, so the second ball can be any of the 7 blue balls.
Number of ways = 6 * 7 = 42.
Number of ways to draw a blue ball and then a white ball:
We have 7 blue balls, so the first ball can be any of the 7 blue balls, and then we have 6 white balls, so the second ball can be any of the 6 white balls.
Number of ways = 7 * 6 = 42.
Number of favorable outcomes = 42 + 42 = 84.
3. Probability of drawing two balls that are white and blue:
Probability = Number of favorable outcomes / Total number of possible outcomes.
Probability = 84 / 120 = 7 / 10 = 0.7.
Therefore, the probability of drawing two balls from the bag that are white and blue is 0.7 or 70%.