Question

In a paper bag, 7 of the 15 marbles are yellow. In a cloth bag, 2 of the 15 marbles are yellow. If Tim randomly draws one marble from each bag, what is the probability that they are both yellow?

Answer 1

`(7)/(15)`×
`(2)/(15)` =
`(14)/(225)`

Explanation:

P(
`Event_(1)`) = choosing yellow marble from paper bag =
`(favourable outcomes)/(possible outcomes)` =
`(7)/(15)`

P(
`Event_(2)`) = choosing yellow marble from cloth bag =
`(favourable outcomes)/(possible outcomes)` =
`(2)/(15)`

∵ Resultant outcome is dependent upon both the events and both events are independent from each other, so we can apply intersection rule [ P(A∩B)=P(A)×P(B) ] here

∴ Probability ( Both marbles are yellow) = P(
`Event_(1)`) × P(
`Event_(2)`) =
`(7)/(15)` ×
`(2)/(15)`