Question

There are 24 red marbles in a bag 68 marbles, and 8 of those marbles are both red and white striped. 27 marbles are white striped and of those marbles, the same 8 marbles would be both red and white striped). Find the probability of drawing out a marble from the bag that is either red or white striped.

(a) \(\frac{12}{35}\)

(b) \(\frac{43}{68}\)

(c) \(\frac{26}{68}\)

(d) \(\frac{32}{55}\)

I have been asked this question in a job interview.

This interesting question is from Addition Theorem on Probability in division Discrete Probability of Discrete Mathematics

Answer 1

The correct option is (b) \(\frac{43}{68}\)

The best I can explain: The “or” indicates finding the probability of a union of events. Let R be the event that a red marble is drawn and W be the event that a striped marble is drawn. R U W is the event that a marble that is either a red and a white striped is drawn. By the rule of sum of probability,

P(R U W) = P(R) + P(W) – p(R ⋂ W) = \(\frac{24}{68} + \frac{27}{68} – \frac{8}{68} = \frac{43}{68}\).

Hence, the probability of drawing a red or white striped marble is \(\frac{43}{68}\).