Question

An urn is filled with marbles of various colors (but each marble only has one color). If the probability of pulling a red marble at random is 1/4 and the probability of pulling a blue marble at random is 1/3, what is the probability that a marble randomly pulled from the urn will be one of those two colors (red or blue)?

Answer 1

`(7)/(12)`

Explanation:

We are given that

The probability of pulling a red marble=
`(1)/(4)`

The probability of pulling a blue marble=
`(1)/(3)`

We have to find the probability that a marble at randomly pulled from the urn will be one of those two colors ( red or blue)

When a marble is of red color then it can not be of blue color .

When a marble is of blue color then it can not be of red color.

`P(Red\cap blue)=0`

We know that

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

A=Red marble

B=Blue marble

`P(A)=(1)/(4)`

`P(B)=(1)/(3)`

Substitute the values then, we get

`P(Red\cup blue)=(1)/(4)+(1)/(3)=(3+4)/(12)=(7)/(12)`

Hence, the probability of pulling red or blue marble from the urn=
`(7)/(12)`