Question

A bag has 2 green marbles, 3 red marbles, and 3 yellow marbles. What is the probabilty that you pick a yellow marble, do not replace it, and pick another yellow marble?

3/28
1/28
9/56
1/8

Answer 1

Probability of picking 2 yellow marbles WITHOUT REPLACEMENT

=
`(3)/(28)`

Explanation:

Number of green marbles = 2

Number of red marbles = 3

Number of yellow marbles = 3

So, the total number of marbles = 2 + 3 + 3 = 8 marbles

Let E : Event of picking a yellow marble from the bag

Now, Probability of an Event E =
`\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}`

⇒ Here,
`P(E) = (3)/(8)`

After picking 1 yellow marble from the bag:

Total marbles left in bag = 8 -1 = 7

Total yellow marbles left in bag = 3 - 1 = 2

Now, the probability of picking the second yellow marble WITHOUT REPLACEMENT =
`\frac{\textrm{Number of favorable outcomes}}{\textrm{Total number of outcomes}}  =  (2)/(7)`

So, the Probability of picking 2 yellow marbles WITHOUT REPLACEMENT

=
`(3)/(8) * (2)/(7)   = (6)/(56) = (3)/(28)`