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)=(58)/(155)`

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

`P(B)=(51)/(155)`

Therefore:

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

Hence, the answer is:

`P(A\text{ }or\text{ }B)=(109)/(155)`