Question

Two marbles are drawn without replacement from a box with 3 White, 2 green, 2 red, and 1 Blue Marble.

Find the probability. Both marbles are white

Answer 1

Answer:
`(3)/(28)`

Explanation:

Given a box contains 3 White ,2 green,2 red & 1 Blue marble

We have to draw two marbles without replacement

therefore for first draw we have 3 white marble to choose among 8 marbles

i.e.

`_(1)^(3)\textrm{C}` choices among the total of
`_(1)^(8)\textrm{C}` options

For second draw we 2 white marbles left therefore no of ways in which a white marble can be choosen is

`_(1)^(2)\textrm{C}`

Therefore required probability is =
`(favourable\ outcome)/(Total\ outcome)`

P
`\left ( required\right )`=
`(3*2)/(8*7)`

P
`\left ( required\right )`=
`(3)/(28)`

Answer 2

`(3)/(28)`

Explanation:

Te meaning of without replacement is once the ball is picked from the stock it cannot be put back

Hre there are total 8 balls and 3 white balls

probability of picking 1st white is
`(3)/(8)`

now only 2 white and total is 7( one ball has already been picked)

therefore probability of picking 2nd white ball is
`(2)/(7)`

both the action are independent events

therefore, probability of picking 2 white balls is
`(3)/(8)` ×
`(2)/(7)`

=
`(3)/(28)`