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?

(i) No. of black marbles = 5 and Total marbles = 7 + 8 + 5 = 20.

Let E₁ be the event of choosing a black marble, then number of favourable outcomes to E₁ = 5

$P(E$1) = \dfrac{\text{No. of favourable outcomes to } E1}{\text{Total no. of possible outcomes}} = \dfrac{5}{20} = \dfrac{1}{4}.

Hence, the probability of choosing a black marble is $\dfrac{1}{4}$.

(ii) Total no. of black and blue marbles = 7 + 5 = 12.

Let E₂ be the event of choosing a black or blue marble, then number of favourable outcomes to E₂ = 12

$P(E$2) = \dfrac{\text{No. of favourable outcomes to } E2}{\text{Total no. of possible outcomes}} = \dfrac{12}{20} = \dfrac{3}{5}.

Hence, the probability of choosing a black or blue marble is $\dfrac{3}{5}$.

(iii) Total no. of blue and white marbles = 7 + 8 = 15.

Let E₃ be the event of choosing a white or blue marble, then number of favourable outcomes to E₃ = 15

$P(E$3) = \dfrac{\text{No. of favourable outcomes to } E3}{\text{Total no. of possible outcomes}} = \dfrac{15}{20} = \dfrac{3}{4}.

Hence, the probability of choosing a not black marble is $\dfrac{3}{4}$.

(iv) Let E₄ be the event of choosing a green marble, then number of favourable outcomes to E₄ = 0, as there is no green marble in the box.

$P(E$4) = \dfrac{\text{No. of favourable outcomes to } E4}{\text{Total no. of possible outcomes}} = \dfrac{0}{20} = 0.

Hence, the probability of choosing a green marble is 0.