among the exames in the examination 30%, 35% & 45% failed in statistics, in maths, & in atleast one of the subjects respectively. one student is selected at random. find the probability that: (a)he has failed in maths, (b)he passed in statistiics if it is known that he has failed in maths

Please give answer

To find the probability in each case, we need to first determine the total number of students who could be selected. Let's assume there are 100 students in total.

(a) Probability that the student has failed in maths:
Since 35% of the students failed in maths, the number of students who failed in maths would be (35/100) * 100 = 35. Therefore, the probability that the student has failed in maths would be 35/100 or 0.35.

(b) Probability that the student passed in statistics, given that he failed in maths:
We know that among the students who failed in at least one subject, the percentage of students failing in statistics is 30%. However, we want to find the probability of passing in statistics given that the student has failed in maths.

Since we are only considering the students who failed in maths, we need to find the probability of passing in statistics among those students. Let's assume that 45 students failed in at least one subject, and out of those students, 35 failed in maths.

To find the probability of passing in statistics, we need to subtract the number of students failing in statistics from the total number of students who failed in maths: 45 - 35 = 10.

Therefore, the probability that the student passed in statistics, given that he failed in maths, would be 10/35 or approximately 0.286 (rounded to three decimal places).