In class X, 20% of the students are boys and 80% of them are girls. The probability that boys passed in mathematics is 0.5 and the probability that girls passed in mathematics is 0.10. One student is selected at random. What is the probability that the selected student is passed inmathematics?

To solve this problem, we need to use the law of total probability. The law of total probability states that the probability of an event can be found by considering all the different ways the event could occur.

Here are the steps to solve the problem:

1. First, we need to find the probability of a student being a boy and passing in mathematics. This is given by the product of the probability of a student being a boy and the probability of a boy passing in mathematics. So, P(Boy and Pass) = P(Boy) * P(Pass|Boy) = 0.20 * 0.50 = 0.10.

2. Next, we need to find the probability of a student being a girl and passing in mathematics. This is given by the product of the probability of a student being a girl and the probability of a girl passing in mathematics. So, P(Girl and Pass) = P(Girl) * P(Pass|Girl) = 0.80 * 0.10 = 0.08.

3. Finally, we add these two probabilities to find the total probability of a student passing in mathematics. So, P(Pass) = P(Boy and Pass) + P(Girl and Pass) = 0.10 + 0.08 = 0.18.

So, the probability that a randomly selected student passed in mathematics is 0.18 or 18%.