Question

A small deck of 5 cards consists of 3 red cards and 2 green cards.

Draw 7 times with replacement.

Find the probability that a red card is drawn exactly 5 times.

Answer 1

0.0776

Explanation:

Number of cards = 5 ; 3 red and 2 green

Since it is with replacement :

Probability of picking a replacement d ball: P(red) = required / total possible outcomes

P(red) = 3 / 5 = 0.6

Using binomial :

P(x =x) = nCx * p(x)^x * (1 - p)^(n - r)

P(x = 5) = 5C5 * (0.6)^5 * 0.4^0

P(x = 5) = 1 * 0.07776 * 1

P(x = 5) = 0.0776