Question

Fifty balls are numbered 1 to 50 and red dot is painted on those balls that are a multiple of 8. the balls are mixed into a bag and on call is randomly chosen. what is the probability that the ball is numbered with a multiple of 10 or has a red dot?

Answer 1

Total number of balls = 50
Balls numbered as multiple of 10 = 5
Balls with red dot on them = 6
Balls numbered as multiple of 10 and having red dot on them = 1 (i.e. Ball with number 40 on it)

Probability of Ball being numbered as multiple of 10 = P(T) = 5/50 = 1/10

Probability of Ball being marked by the dot = P(D) = 6/50 = 3/25

Probability of Ball being numbered as multiple of 10 and having a red dot on it = P (T ∩ D) = 1/50

The "or" ,"union" of two events can be expressed as:

P(T ∪ D) = P(T) + P(D) - P (T ∩ D)

Using the values, we get:

P(T ∪ D) = $\frac{1}{10} + \frac{3}{25}- \frac{1}{50}=1/5$

Thus, the probability that the ball is numbered with a multiple of 10 or has a red dot is 1/5 or 0.2