a bag contains 3 red, 6 white and 7 blue balls. What is the probility that two balls drawn are white and blue?
16 total to start
I could draw a white, then blue
6/16 * 7/15
or
I could draw a blue, then white
7/16 * 6/15
add them
2(42/240) = .35
To find the probability of drawing two balls, one white and one blue, we need to calculate the probability of drawing a white ball and then a blue ball.
Step 1: Calculate the probability of drawing a white ball.
The bag contains a total of 3 red, 6 white, and 7 blue balls. The probability of drawing a white ball on the first draw is:
P(White) = Number of white balls / Total number of balls
= 6 / (3 + 6 + 7)
= 6 / 16
= 3 / 8
Step 2: Calculate the probability of drawing a blue ball.
Once you have drawn a white ball, the total number of balls in the bag has reduced by 1, so there are 15 balls left in the bag. The probability of drawing a blue ball on the second draw, after having drawn a white ball, is:
P(Blue) = Number of blue balls left / Total number of balls left
= 7 / 15
Step 3: Calculate the probability of drawing a white and then a blue ball.
The probability of drawing a white ball and then a blue ball is the product of the probability of each event occurring, since the events are independent:
P(White and Blue) = P(White) × P(Blue)
= (3/8) × (7/15)
= 21 / 120
= 7 / 40
Therefore, the probability of drawing two balls, one white and one blue, is 7/40.
To find the probability of drawing two balls, one white and one blue, from the given bag, we need to determine the total number of possible outcomes and the number of favorable outcomes.
First, let's calculate the total number of balls in the bag:
Total number of balls = number of red balls + number of white balls + number of blue balls
Total number of balls = 3 red balls + 6 white balls + 7 blue balls
Total number of balls = 16 balls
Now, let's calculate the number of favorable outcomes, i.e., the number of ways to choose one white ball and one blue ball:
Number of ways to choose one white ball = number of white balls = 6 white balls
Number of ways to choose one blue ball = number of blue balls = 7 blue balls
To find the total number of favorable outcomes, we multiply these two numbers together:
Total number of favorable outcomes = number of ways to choose one white ball * number of ways to choose one blue ball
Total number of favorable outcomes = 6 white balls * 7 blue balls
Total number of favorable outcomes = 42
Finally, let's calculate the probability by dividing the number of favorable outcomes by the total number of outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 42 / 16
Probability = 2.625
The probability of drawing two balls, one white and one blue, from the bag is 2.625 (or 105/40)