Mathematics 2005 JAMB Past Questions - Question 50: What is the probability that an integer x(1  ≤ x  ≤ 20) chosen at random is divisible by both 2 and 3?

Correct Answer

C

Explanation

To find the probability of obtaining two blue or two red balls when two balls are selected from the box with replacement, we need to calculate the probability of each event separately and then add them together.Probability of selecting two blue balls:The probability of selecting a blue ball on the first draw is 5/30 (since there are 5 blue balls out of a total of 30 balls). Since we are replacing the ball after each draw, the probability of selecting a blue ball on the second draw is also 5/30. Therefore, the probability of selecting two blue balls is (5/30) * (5/30) = 25/900.Probability of selecting two red balls:Similarly, the probability of selecting a red ball on the first draw is 3/30, and the probability of selecting a red ball on the second draw is also 3/30. Therefore, the probability of selecting two red balls is (3/30) * (3/30) = 9/900.Now, we can add the probabilities of the two events to find the overall probability:Probability of obtaining two blue or two red balls = Probability of two blue balls + Probability of two red balls                                                = 25/900 + 9/900                                                = 34/900                                                = 17/450Therefore, the probability of obtaining two blue or two red balls is 17/450.