Question

There are 5 green, 3 black, and 2 white marbles in an urn. If you draw 3 marbles, what is the probability that there will be no black marbles drawn if you draw with replacement?

Answer 1

5 green, 3 black, and 2 white marbles

Total number of marbles = 5 + 3 + 2 = 10

P[ black marble ] = number of black marbles / total number of marbles

P[ black marble ] = 3/10

P[ black marble ] = 0.3

P[ no black marble ] = 1 - P[ black marble ]

P[ no black marble ] = 1 - 0.3

P[ no black marble ] = 0.7

With replacement case

P[ 3 drawn without black marble ] = P[ no black marble ]^3

P[ 3 drawn without black marble ] = 0.7^3

P[ 3 drawn without black marble ] = 0.343