Question

A bag of marbles contains 12 red marbles 8 blue marbles and 5 green marbles. If three marbles are pulled out find each of the probabilities. Find the probability of pulling three green marbles out with replacement

Answer 1

$|\Omega|=25\cdot24\cdot23=13800\\ |A|=5\cdot4\cdot3=60\\\\ P(A)=\dfrac{60}{13800}=\dfrac{1}{230}\approx0.4\%$

Answer 2

The probability of an event is calculated as = $\frac{Favorable outcomes}{Total number of outcomes}$

Here, the total number of outcomes = 12 red marbles + 8 blue marbles + 5 green marbles

So, total marbles = 25 marbles

Number of favorable or green marbles = 5 marbles

Probability of three green marbles if drawn with replacement = $\frac{Number of favorable or green marbles}{Total number of marbles}$ ×$\frac{Number of favorable or green marbles}{Total number of marbles}$ × $\frac{Number of favorable or green marbles}{Total number of marbles}$

Probability of three green marbles if drawn with replacement = $\frac{5}{25}$ × $\frac{5}{25}$ × $\frac{5}{25}$

Probability of three green marbles if drawn with replacement = $\frac{1}{125}$