In a class of 25 students, 12 like maths(M), 9 like science(S) and 3 like both. Find the probability that a randomly selected student likes neither maths nor science.

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UpStudy AI · Accepted Answer

To find the probability that a randomly selected student likes neither maths nor science, we can use the principle of inclusion-exclusion.

Let:
- $$ n(M) $$ = number of students who like maths = 12
- $$ n(S) $$ = number of students who like science = 9
- $$ n(M \cap S) $$ = number of students who like both maths and science = 3

First, we need to find the number of students who like either maths or science or both, which is given by:

$$
n(M \cup S) = n(M) + n(S) - n(M \cap S)
$$

Substituting the values:

$$
n(M \cup S) = 12 + 9 - 3 = 18
$$

Now, the number of students who like neither maths nor science is the total number of students minus those who like either or both subjects:

$$
n(\text{neither}) = \text{Total students} - n(M \cup S) = 25 - 18 = 7
$$

Now, we can find the probability that a randomly selected student likes neither maths nor science:

$$
P(\text{neither}) = \frac{n(\text{neither})}{\text{Total students}} = \frac{7}{25}
$$

Thus, the probability that a randomly selected student likes neither maths nor science is:

$$
\frac{7}{25}
$$
The probability is $$ \frac{7}{25} $$.

In a class of 25 students, 12 like maths(M), 9 like science(S) and 3 like both. Find the probability that a randomly selected student likes neither maths nor science.

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