A box contains 4 green 6 red 1 yellow 7 blue and 8 purples b

A box contains 4 green, 6 red, 1 yellow, 7 blue, and 8 purples buttons. Four buttons are drawn from the box simultaneously. a) What is the probability that none of the buttons are red? b) What is the probability that all four buttons are the same color? c) What is the probability that all four buttons are different colors?

Solution

there are total 26 buttons.

probability of selecting 1 red = 6/26

a) none of the button is red = 4C0*(6/26)^0*(20/26)^4 = 0.350

B) ALL 4 ARE SAME COLOUR , PROBABILITY OFALL GREEN = 4/26^4 = 0.0005

PROBABILITY OF ALL BLUE = 7/26^4= 0.005

PROBABILITY OFALL PURPLES = 8/26^4 = 0.008

PROBABILITY OF ALL RED = 6/26^4 = 0.002

SO PROBABILITY OF SAME COLOUR = 0.0155( ADD ALL THE PROBABILITY)

C)PROBABILITY ALL ARE DIFFERENT COLORS = 1 - PROBABILITY ALL ARE SAME COLOR

= 1 - 0.0155 = 0.9845

D)AT LEAST 3 ARE PURPLE MEANS 3 PURPLE + 4 PURPLE

4C3(8/26)^3*(18/26)^1 + 4C4*(8/26)^4*(18/26)^0

= 0.080 + 0.008 = 0.088