6. A bowl contains 10 red balls, 10 green balls and 10 white balls. a. What is the probability of drawing 2 white balls with replacement? b. What is the probability of drawing 2 white balls without replacement?
when balls are replaced
Prob(2white) = (10/30)(10/30) = 1/9
without replacement
prob(2white) = (10/30)(9/29) = 3/29
78
where is the fu*n solution
Probability of getting 2 white balls (W) with replacement is :
P(W) = ( (10/30) * (10/30) ) = 1/9
Probability of getting 2 white balls (W) without replacement is :
P(W) = ( (10/30) * (9/29) ) = 3/29
To find the probability of drawing 2 white balls with replacement, we consider that after each draw, the ball is placed back in the bowl, making the total number of balls remain the same.
a. Probability of drawing 2 white balls with replacement:
The probability of drawing a white ball with replacement is the number of white balls divided by the total number of balls.
Number of white balls = 10
Total number of balls = 10 red balls + 10 green balls + 10 white balls = 30
Probability = 10/30 * 10/30 = 1/9
To find the probability of drawing 2 white balls without replacement, we need to consider that after each draw, the ball is not replaced into the bowl, thus reducing the total number of balls.
b. Probability of drawing 2 white balls without replacement:
The probability of drawing the first white ball is the number of white balls divided by the total number of balls.
Number of white balls = 10
Total number of balls = 10 red balls + 10 green balls + 10 white balls = 30
Probability of drawing the first white ball = 10/30
After drawing the first white ball, there are now 9 white balls remaining out of a total of 29 balls.
The probability of drawing the second white ball is the number of remaining white balls divided by the remaining total number of balls.
Remaining number of white balls = 9
Remaining total number of balls = 29
Probability of drawing the second white ball = 9/29
To find the combined probability, we multiply the probabilities of each event:
Probability = (10/30) * (9/29) = 3/29
So, the probability of drawing 2 white balls without replacement is 3/29.