Among the examinees in a examination 30% 35% and 45% failed in statistics, in mathematics and in at least some of the subjects respectively. An examinee is selected at a random. Find the probability that he failed in mathematics only ?

Question

Answer

**Solution:**

Given,
- 30% failed in Statistics
- 35% failed in Mathematics
- 45% failed in at least some of the subjects

Let's assume that there are 100 examinees in the examination.

So,
- number of examinees who failed in Statistics = 30% of 100 = 30
- number of examinees who failed in Mathematics = 35% of 100 = 35
- number of examinees who failed in at least some of the subjects = 45% of 100 = 45

Now, we need to find the probability that an examinee failed in Mathematics only.

Let's assume that there are x examinees who failed in Mathematics only.

So,
- number of examinees who failed in both Statistics and Mathematics = (30-x)
- number of examinees who failed in at least Mathematics = (35-x)

From the given information, we know that 45% of the examinees failed in at least some of the subjects. So, we can write the equation as:

(30-x) + x + (35-x) + (number of examinees who passed in both Statistics and Mathematics) = 55

Simplifying the above equation, we get:

x = 10

So, there are 10 examinees who failed in Mathematics only.

Therefore, the probability that an examinee failed in Mathematics only is:

Number of examinees who failed in Mathematics only / Total number of examinees

= x / 100

= 10 / 100

= 0.1

Hence, the probability that an examinee failed in Mathematics only is 0.1.

Answer

0.25

Answer

P(s) = 30% ; p(M) = 35% ;

p(s or m) = 45%

p(s or m) = p(S) + P(M) - p(s and m)

45% = 30% + 35% - p(s and m)

p(s and m) = 65%- 45% = 20%

probability that he failed in mathematics only is p(M or S')

P( M OR S') = P(M) - P( M OR S)

P(M OR S') = 35% - 20% = 15%= 0.15

Answer

35/100=0.35

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