Question

(i) A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?

(ii) Suppose the bulb drawn in (i) is not defective and not replaced. Now bulb is drawn at random from the box, find the probability that it bears (i) a two digit number (ii) a perfect square number (ii) a number divisible by 5.

Answer 1

(i) Total number of possible outcomes, n(S) = 20 

Number of favorable outcomes, 

n(E) = 4

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{20}\) = \(\frac{1}{5}\)

(ii) Total number of possible outcomes, n(S) = 19 

Number of favorable outcomes, 

n(E) = 15

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{15}{19}\)