Statistics/Probability question

Question

Four balls with different colors: red, yellow, green, and blue, are placed in a box. Every time Amy picks up a ball, then puts it back to the box and draws one again, repeating it five times.  a) What is the probability that she gets at least four red balls in the five draws? b) What is the probability that she will get no more than two red balls in the five draws?

Answer 1

a) P(at least 4 red) = P(4 red) + P(5 red)

= 5 X (1/4)^4 X (3/4) + (1/4)^5

 

b) P(no more than 2 red) = P(0 red) + P(1 red) + P(2 red)

= (3/4)^5 + 5 X (1/4) X (3/4)^4 + 10 X (1/4)^2 X (3/4)^3

 

The factors of 5 are to account for the possibility of 1 not red in 5 different positions in a) and 5 different positions

for 1 red in b. The factor of 10 covers all possible positions of 2 reds in 5 slots in b).