What is the probability that it will be

A box contains 7 blue, 8 white, and 5 black marbles. If a marble is drawn at random from the box, what is the probability that it will be
(i) black?
(ii) blue or black?
(iii) not black?
(iv) green?

Solution:

Total number of marbles in the box
= 7 + 8 + 5 = 20
Since, a marble is drawn at random from the box
(i) Probability (of a black Marble)
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 5 }{ 20 }$
= $\\ \frac { 1 }{ 4 }$
(ii) Probability (of a blue or black marble)
P(E) = $\frac { Number\quad of\quad favourable\quad outcome }{ Number\quad of\quad possible\quad outcome }$
= $\\ \frac { 7+5 }{ 20 }$
= $\\ \frac { 12 }{ 20 }$
= $\\ \frac { 3 }{ 5 }$
(iii) Probability (of not black marble)
= 1 – P (of black 1)
= $1- \frac { 1 }{ 4 }$
= $\\ \frac { 4-1 }{ 4 }$
= $\\ \frac { 3 }{ 4 }$
(iv) P (of a green marble) = 0
(∴ Since, a box does not contain a green marble,
so the probability of green marble will be zero)