A box contains 2 white and 3 blue identical marbles. If two marbles are picked at random, one after the other without replacement, what is the probability o...

A box contains 2 white and 3 blue identical marbles. If two marbles are picked at random, one after the other without replacement, what is the probability of picking two marbles of different colors?

Answer Details

There are a total of 5 marbles in the box, 2 of which are white and 3 are blue. If two marbles are picked one after the other without replacement, there are two possible scenarios: either a white marble is picked first or a blue marble is picked first. Case 1: A white marble is picked first. In this case, there are 4 marbles left, out of which 3 are blue. Therefore, the probability of picking a blue marble after picking a white marble is 3/4. Case 2: A blue marble is picked first. In this case, there are 4 marbles left, out of which 2 are white. Therefore, the probability of picking a white marble after picking a blue marble is 2/4 or 1/2. Since there are two possible scenarios and each scenario is mutually exclusive, we can add the probabilities of the two scenarios to get the probability of picking two marbles of different colors: Probability = (Probability of picking a white marble first x Probability of picking a blue marble second) + (Probability of picking a blue marble first x Probability of picking a white marble second) Probability = (2/5 x 3/4) + (3/5 x 1/2) Probability = 3/10 + 3/10 Probability = 6/10 or 3/5 Therefore, the probability of picking two marbles of different colors is 3/5 or 0.6. Answer is the correct answer.