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)$$P(brw)=\frac{8}{20}*\frac{7}{20}*\frac{5}{20}$$P(brw)=\frac{280}{8000}=\frac{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)=\frac{7}{20}*\frac{7}{20}*1$$p(rrx)=\frac{49}{400}$$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-(\frac{5}{20})$$1-p(w)=\frac{3}{4}$$1-p(w)=\frac{3}{4}=0.75$

the probability that none is white is 0.75 or 75%