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
i think that the question is not complete but it could be p(fail in math)= 35%
we don't know the sample size,or pop. size, even not the the x.
To find the probability of a specific event, we need to know the total number of possible outcomes and the number of favorable outcomes.
In this case, we have three subjects: statistics, maths, and at least one subject. Let's find the probability for each part of the question separately:
(a) Probability that he has failed in maths:
Since 35% failed in maths, the probability of failing in maths is 0.35.
(b) Probability that he passed in statistics given that he failed in maths:
We know that 45% failed in at least one of the subjects, which means that 100% - 45% = 55% passed in all subjects.
To find the probability that he passed in statistics given that he failed in maths, we need to subtract the probability of failing in both maths and statistics from the probability of failing in maths.
The probability of failing in both maths and statistics is calculated by multiplying the probabilities of failing in each subject, so it is 0.35 * 0.30 = 0.105.
Therefore, the probability of passing in statistics given that he failed in maths is 0.35 - 0.105 = 0.245.
Remember, the total number of possible outcomes is always 1, so the sum of probabilities of all possible events should equal 1.
Please note that the percentages given in the question need to be converted to probabilities by dividing them by 100.