There are 21 pupils who study Maths, 29 pupils who study french, 26 pupils who study history. there are 4 pupils who study both maths and french. 10 pupils who study both french and history and 3 pupils who study both maths and history. there 1 pupil who studies all three subjects.

two different pupils are selected at random. find the probability that they both study history.

Help, i do not understand this question.

If we consider the selections as independent events, then since there are

(21+29+26)-(4+10+3)+(1) = 60

students, of whom 26 study history, the chance of any student's studying history is 13/30.

So, the chance of both is (13/30)^2

Sure, let's break down the information given:

- There are 21 pupils who study Maths.
- There are 29 pupils who study French.
- There are 26 pupils who study History.
- 4 pupils study both Maths and French.
- 10 pupils study both French and History.
- 3 pupils study both Maths and History.
- There's 1 pupil who studies all three subjects.

To find the probability that two randomly selected pupils both study History, we need to determine the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:
When two pupils are selected at random, the total number of outcomes can be calculated using the concept of combinations. We need to choose 2 pupils from a total of 21 + 29 + 26 pupils, which is equal to 76 pupils.
The total number of outcomes is given by the formula C(76, 2) = 76! / 2!(76 - 2)! = 76! / (2! × 74!) = (76 × 75) / (2 × 1) = 2,850.

Number of favorable outcomes:
We want to find the number of ways to choose two pupils who both study history. There are 26 pupils who study history, so the number of ways to choose 2 pupils out of 26 is given by C(26, 2) = 26! / 2!(26 - 2)! = 325.

Now we can find the probability:
The probability is the number of favorable outcomes divided by the number of total outcomes:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 325 / 2850
Probability ≈ 0.114 or 11.4%

So, the probability that two randomly selected pupils both study History is approximately 0.114 or 11.4%.