Question

There are 8 black balls and 6 red balls in an urn. If 4 balls are drawn without replacement, what is the probability that at least 3 black balls are drawn? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Binomial Distribution to be applied to find the required .

If 'X' is the random variable representing the number of successes, the probability of getting ‘r’ successes and ‘n-r’ failures, in 'n' trails, ‘p’ probability of success ‘q’=(1-p) is given by the probability function

Number of black balls in the urn = 8

Number of red balls in the urn =6

Total number of balls = 14

Probability of drawing a black ball : p = Number of black balls in the urn / Total number of balls = 8/14 = 0.5714

q = 1-p = 1-0.5714 = 0.4286

Number of Balls drawn :n = 4

X : Number of black balls drawn

'X' Follows a Binomial distribution with n=4 and p =  0.5714 with probability function

Probability that at least 3 black balls are drawn = P(X3) = P(X=3) + P(X=4)

P(X=3) + P(X=4) = 0.3198 + 0.1066 = 0.4264

P(X3) = P(X=3) + P(X=4) = 0.4264

Probability that at least 3 black balls are drawn = 0.4264