Question

A bag containing 20 small identical objects, 8 of them are black, 7 are red and the rest are white. If three of the objects are selected at random from the bag at once, find the probability that:i) one is black, one is red and the remaining one is white.ii) exactly two are red.iii)none of them is white.

Answer 1

we have

20 objects

8 black

7 red

rest white

20-8-7= 5

5 white

since we are selecting 3 object at once

1) probability that one is black, one is red and the remaining one is white.

`P(brw)=p(b)*p(r)*p(w)`
`P(brw)=(8)/(20)*(7)/(20)*(5)/(20)`
`P(brw)=(280)/(8000)=(7)/(200)\frac{}{}`
`P(brw)=0.035`

1) probability one is black, one is red and the remaining one is white. is 0.035 or 3,5%

ii) exactly two are red.

`p(rrx)=p(r)*p(r)*p(X)`

lets assume x is any ball

then p(x) is the probability of ge any ball = 1

`p(rrx)=(7)/(20)*(7)/(20)*1`
`p(rrx)=(49)/(400)`
`p(rrx)=0.1225`

the probability of exactly two are red. is 0.1225 or 12,25%

iii)none of them is white.​

`1-p(w)=1-((5)/(20))`
`1-p(w)=(3)/(4)`
`1-p(w)=(3)/(4)=0.75`

the probability that none is white is 0.75 or 75%