Question

A bag contains two red marbles, four green ones, one transparent one, two yellow ones, and two orange ones. You select three at random. Compute the probability of the given event. (Enter your probability as a fraction.) You have selected all the red ones.

Answer 1

Solution:
Given in the question
A bag contains
Red marbles = 2
Green marbles = 4
Transparent = 1
Yellow = 2
Orange = 2
Total number of Marbles = 2+4+1+2+2 = 11 marbles
If select 3 marbles at random than we need to calculate the probability that we have selected all the red marbles.
Probability can be calculated as
Probability = (Total number of to select 3 balls in which all the red ones)/ Total number of ways to select 3 marbles out of 11
Total number of ways to select 3 marbles out of 11 marbles = 11*10*9 = 990
Total number of ways to select 2 red balls and 1 any color marble = 2*1*9 = 18
So Probability = (Total number of to select 3 balls in which all the red ones)/ Total number of ways to select 3 marbles out of 11 = 18/990 = 1/55
P(All red ones selected) = 1/55