Question

Two boxes are placed in front of you. Box A contains 4 white and 2 black

marbles, and Box B contains 3 white and 7 black marbles. You select one of
the two boxes at random and then select one marble from that box at
random. What is the probability that the marble you select is black?

Answer 1

The probability that the marble you select is black is 0.5167

Explanation:

Let,

`E_1` the probability of selecting one marble from box A

`E_2` the probability of selecting one marble from box B

`BB_1` be the probability of selecting black marble from box A

`BB_2` be the probability of selecting black marble from box B

Now

`P(E_1) = (1)/(2)`

`P(E_2) = (1)/(2)`

`P(BB_1) = (2)/(6)`

`P(BB_2) = (7)/(10)`

P(Selecting a Black Marble ) =
`(P(E_1) * P(BB_1))+(P(E_2) * P(BB_2))`

=>
`((1)/(2) * (2)/(6))+((1)/(2) * (7)/(10))`

=>
`((2)/(12))+((7)/(20))`

=>
`((1)/(6))+((7)/(20))`

=>
`(20 + 42)/(120)`

=>
`(62)/(120)`

=>
`(31)/(60)`

=>0.5167