Question

What is the probability of drawing yellow marble followed by a red marble from a bag containing 12 yellow marbles, 16 red marbles, and 15 green marbles if the first marble is not replaced?

a. 18/43
b. 32/301
c. 192/1,849

Answer 1

Option B

Probability of drawing yellow marble followed by a red marble is
`(32)/(301)`

Solution:

Given that a bag containing 12 yellow marbles, 16 red marbles, and 15 green marbles

So total number of marbles = 12 + 16 + 15 = 43

To find: probability of drawing yellow marble followed by a red marble if the first marble is not replaced

The probability of an event is given as:

`probability =\frac{\text { number of favorable outcomes }}{\text { total number of possible outcomes }}$`

probability of drawing yellow marble followed by a red marble if the first marble is not replaced:

First we pick up yellow marble.

Number of favorable outcomes = 12 yellow marbles

Total number of possible outcomes = 43 marbles

`\text{ probability} = (12)/(43)`

Now we have to pick red marble

But first marble is not replaced

So we have 43 - 1 = 42 number of possible outcomes

Favorable outcomes = 16 red marbles

`\text{ probability} = (16)/(42)`

So probability of drawing yellow marble followed by a red marble is:

`\text[ probability } = (12)/(43) * (16)/(42) = (32)/(301)`

Thus probability of drawing yellow marble followed by a red marble is
`(32)/(301)`