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 $\frac{32}{301}$

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

$\text{ probability} = \frac{12}{43}$

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

$\text{ probability} = \frac{16}{42}$

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

$\text[ probability } = \frac{12}{43} \times \frac{16}{42} = \frac{32}{301}$

Thus probability of drawing yellow marble followed by a red marble is $\frac{32}{301}$