An urn contains four red marbles and six blue marbles. Two marbles are chosen in order with first marble being replaced after its colour is noted. The probability of choosing marbles of different colours is
To find the probability of choosing marbles of different colors, we first need to find the probability of choosing a red marble followed by a blue marble, as well as the probability of choosing a blue marble followed by a red marble.
The probability of choosing a red marble on the first draw is 4/10, since there are 4 red marbles out of a total of 10 marbles.
After replacing the first marble, there are still 4 red marbles out of a total of 10 marbles, so the probability of choosing a blue marble on the second draw is 6/10.
Therefore, the probability of choosing a red marble followed by a blue marble is (4/10) * (6/10) = 24/100 = 12/50.
Similarly, the probability of choosing a blue marble followed by a red marble is (6/10) * (4/10) = 24/100 = 12/50.
Since these are the only two possible outcomes for choosing marbles of different colors, we can add these probabilities together to get the overall probability:
(12/50) + (12/50) = 24/50 = 12/25.
Therefore, the probability of choosing marbles of different colors is 12/25.
To calculate the probability of choosing marbles of different colors, we need to consider the possible outcomes and then determine the favorable outcomes.
First, let's calculate the total number of possible outcomes. Since there are 10 marbles in total and we are choosing two marbles with replacement (replacing the first marble after its color is noted), the total number of possible outcomes is:
10 * 10 = 100
Now, let's calculate the number of favorable outcomes. In order to choose marbles of different colors, we have two cases:
Case 1: The first marble chosen is red and the second marble chosen is blue.
The probability of choosing a red marble on the first draw is 4/10, and the probability of choosing a blue marble on the second draw is also 6/10. So, the probability of this case is (4/10) * (6/10) = 24/100.
Case 2: The first marble chosen is blue and the second marble chosen is red.
The probability of choosing a blue marble on the first draw is 6/10, and the probability of choosing a red marble on the second draw is 4/10. So, the probability of this case is (6/10) * (4/10) = 24/100.
Now, let's add the probabilities of the two cases to find the total number of favorable outcomes:
24/100 + 24/100 = 48/100
Therefore, the probability of choosing marbles of different colors is 48/100, which can also be expressed as 12/25 or 0.48.