Question

A jar contains four blue marbles and two red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event. Both of the selected marbles are red. The probability that both of the selected marbles are red is _______.

Answer 1

Blue marbles = 4

Red marbles = 2

There are a total of 6 marbles in the bag. If we draw one and don't replace it, there are 5 marbles left in the bag during our second choice...

`\begin{gathered} pr(\text{blue)}=(4)/(6) \\ pr(\text{red)}=(2)/(6) \end{gathered}`
`Pr(Both\text{red)}=(2)/(6)*(1)/(5)=(2)/(30)=(1)/(15)`

we have 2/6 for our first draw and 1/5 for our second draw...multiplied together, we have a 1/15 chance of drawing a red marble and another red marble without replacing any after each draw.

Therefore the probability that both of the selected marbles are red is 1/15 == 0.067