To calculate the probability that two students picked at random attend chess club and one is in year 7 and the other in year 8, we need to use the concept of conditional probability. Let's break down the steps:
Step 1: Find the total number of students who attend chess club.
We can see from the table that 12 year 7 students and 10 year 8 students attend chess club, so the total number of students who attend chess club is 12 + 10 = 22.
Step 2: Find the probability that the first student is in year 7 and the second student is in year 8.
The probability that the first student is in year 7 is 22/40 because there are 22 students who attend chess club out of a total of 40 students (the sum of all the numbers in the table). The probability that the second student is in year 8 is 18/39 because there are 18 students in year 8 who do not attend chess club out of a total of 39 students who do not attend chess club (the total number of students in year 8 minus the number of students who attend chess club).
Step 3: Find the probability that one student is in year 7 and the other student is in year 8.
To find the probability that one student is in year 7 and the other student is in year 8, we need to multiply the probabilities from steps 1 and 2, and then multiply by 2 (since we can pick the students in either order):
(22/40) * (18/39) * 2 ≈ 0.28
Therefore, the probability that two students picked at random attend chess club and one is in year 7 and the other in year 8 is approximately 0.28.