Question

a box contains 46 red marbles, 58 white marbles, and 51 blue marbles.if a marble is randomly selected from the box,what is the probability that it is white or blue express your answer as a simplified fraction or decimal rounded to four decimal places

Answer 1

Given that the box contains 46 red marbles, 58 white marbles, and 51 blue marbles, you know that the total number of marbles the box contains is:

$46+58+51=155$

In this case, let be A the event in which the randomly selected marble from the box is white, and B the event in which the randomly selected marble from the box is blue.

Since those events are independent, you can set up that the probability of randomly selecting a white marble or blue marble from the box is:

$P(A\text{ }or\text{ }B)=P(A)+P(B)$

Knowing that there are 58 white marbles, you can determine that:

$P(A)=\frac{58}{155}$

And knowing that there are 51 blue marbles, you can determine that:

$P(B)=\frac{51}{155}$

Therefore:

$P(A\text{ }or\text{ }B)=\frac{58}{155}+\frac{51}{155}$$P(A\text{ }or\text{ }B)=\frac{109}{155}$

Hence, the answer is:

$P(A\text{ }or\text{ }B)=\frac{109}{155}$