A bag contain 5 white 7 red 5 black balls.if 4 balls are drwn one by one with replacmment tha probability that none is white
Since the ball is returned, these are independent events
prob(not white) = 12/17
we want this 4 times in a row, so
prob(your event) = (12/17)^4
To find the probability that none of the 4 drawn balls is white when drawn with replacement, we need to consider the total number of possible outcomes and the favorable outcomes.
Total number of possible outcomes: There are a total of 17 balls in the bag (5 white + 7 red + 5 black).
Favorable outcomes: We are interested in the cases where none of the drawn balls is white. Since there are 5 white balls, we can calculate the number of ways to draw 4 non-white balls as (12 choose 4).
Now, let's calculate the probability using these values:
Total number of possible outcomes = 17
Number of favorable outcomes = (12 choose 4)
P(none is white) = Number of favorable outcomes / Total number of possible outcomes
To calculate (12 choose 4), we can use the combination formula:
(12 choose 4) = 12! / (4!(12-4)!) = (12*11*10*9)/(4*3*2*1) = 495
Therefore, P(none is white) = 495 / 17 ≈ 0.876
So, the probability that none of the 4 balls drawn with replacement is white is approximately 0.876.