Question

A bag contains 8 b l a c k marbles, 5 w h i t e marbles, and 3 y e l l o w marbles. If a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a b l a c k marble and then a y e l l o w marble? b. A bag contains 5 r e d marbles, 3 y e l l o w marbles, and 8 w h i t e marbles. If two different marbles are drawn from the bag , what is the probability of drawing first a r e d marble and then a w h i t e marble?

Answer 1

(a).
`Probability=(3)/(32)`

(b).
`Probability=(1)/(6)`

Explanation:

(a).

The number of Black marbles in the bag = 8

Number of White marbles in the bag = 5

Number of Yellow marbles in the bag = 3

Total marbles in the bag = 16

The probability is given by,

`Probability=(Favourable\ outcomes)/(Total\ Possibilities)`

So,

Probability of drawing a Black Marble first is,

`Probability=(8)/(16)=(1)/(2)`

Now replacement is done.

So,

Probability of drawing Yellow Marble second is,

`Probability=(3)/(16)`

So,

Probability is given by,

`Probability=(1)/(2)* (3)/(16)\\Probability=(3)/(32)`

Therefore, the probability is,

`Probability=(3)/(32)`

(b).

Number of Red marbles = 5

Number of Yellow marbles = 3

Number of White marbles = 8

Total marbles = 46

Probability of drawing a Red marble first is given by,

`Probability=(5)/(16)`

And,

Probability of drawing a White marble second is given by,

`Probability=(8)/(15)`

As, there is no replacement.

So,

Probability is given by,

`Probability=(5)/(16)* (8)/(15)\\Probability=(1)/(6)`

Therefore, the Probability is given by,

`Probability=(1)/(6)`