Question

# A bag contains 5 red marbles, 7 white marbles, and 7 blue marbles. You draw 3...

A bag contains 5 red marbles, 7 white marbles, and 7 blue marbles. You draw 3 marbles out at random, without replacement. What is the probability that all the marbles are red? These are very small probabilities so enter your answer with four significant digits. For example: 0.0001345.

The probability that all the marbles are red is ______ .

What is the probability that none of the marbles are red?
The probability that none of the marbles are red is ________ .

solution:

the details of marbles as follows:

red marbles = 5

white marbles = 7

blue marbles = 7

total marbles = 19

it is given that the three marbles are drawn without replacement.

a)

we have to find P(all marbles are red)

number of ways of selecting the 3 marbles out of 5 red marbles = total number of ways of selecting 3 marbles out of total 19 marbles = so, P(all marbles are red) = 10 / 969 = 0.01032

b)

probability tha the none of the marble is red = P(none is red)

number of marbles except red = 19 - 5 = 14

number of ways of selecting 3 none red marbles out of 14 = P(none is red) = 364 / 969 = 0.3756