Question

Miranda has a bag of marbles with 5 blue marbles, 1 white marbles, and 1 red marbles. Find the following probabilities of Miranda drawing the given marbles from the bag if the first marble(s) is(are) not returned to the bag after they are drawn.

a) A Blue, then a red Preview
b)A red, then a white Preview
c) A Blue, then a Blue, then a Blue

Answer 1

(a)
`(5)/(7),(1)/(6)` (b)
`(1)/(7),(1)/(6)` (c)
`(5)/(7),(2)/(3),(3)/(5)`

Explanation:

GIVEN: Miranda has a bag of marbles with
`5` blue marbles,
`1` white marbles, and

TO FIND: a) A Blue, then a red Preview

,b)A red, then a white Preview

,c) A Blue, then a Blue, then a Blue.

SOLUTION:

Total marbles in bag
`=7`

(a)

Probability of drawing blue marble
`=\frac{\text{total blue marble}}{\text{total marbles}}`

`=(5)/(7)`

As marble is not returned to bag,

Probability of drawing red marble
`=\frac{\text{total red marble}}{\text{total marbles}}`

`=(1)/(6)`

(b)

Probability of drawing red marble
`=\frac{\text{total red marble}}{\text{total marbles}}`

`=(1)/(7)`

As marble is not returned to bag,

Probability of drawing white marble
`=\frac{\text{total white marble}}{\text{total marbles}}`

`=(1)/(6)`

(c)

Probability of drawing blue marble
`=\frac{\text{total blue marble}}{\text{total marbles}}`

`=(5)/(7)`

As marble is not returned to bag,

Probability of drawing second blue marble
`=\frac{\text{total blue marble}}{\text{total marbles}}`

`=(4)/(6)=(2)/(3)`

As marble is not returned to the bag

Probability of drawing third blue marble
`=\frac{\text{total blue marble}}{\text{total marbles}}`

`=(3)/(5)`