Question

There are 4 yellow marbles, 6 green marbles, and 5 blue marbles in a jar. Event A is defined as drawing a green marble from the jar on the first draw. Event B is defined as drawing a yellow marble on the second draw.

If two marbles are drawn from the bag, one after the other without replacement, what is P(B|A) expressed in simplest form?

A)4/15
B)2/7
C)1/3
D)2/5

Answer 1

its acttually B

Explanation:

Answer 2

Answer:(a)

Explanation:

Given

There are 4 yellow, 6 green and 5 blue marbles

We have to find
`P(B\mid A)` i.e. conditional probability of B given that A is occurred.

`P(B\mid A)` is given by

`P(B\mid A)=(P(A\cap B))/(P(A))`

Also A=drawing a green marble

B=drawing a yellow marble

Total no of marbles
`=4+6+5=15`

So,

`P(A)=(6)/(15)`

similarly
`P(B)=(4)/(15)`

`P(A\cap B)=P(A)* P(B)`

`P(A\cap B)=(6)/(15)* (4)/(15)`

`P(A\cap B)=(24)/(225)`

Substituting the values in the formula

`P(B\mid A)=((24)/(225))/((6)/(15))`

`P(B\mid A)=(24)/(6)* (15)/(225)`

`P(B\mid A)=(4)/(15)`