1. There are 40 pupils in a class. 30 of them study Biology, 22 study Physics and 21 study Chemistry. 15 study Physics and Biology, 10 study Physics and Chemistry, 13 study Biology and Chemistry, 2 study Physics only, 3 study Chemistry only and 7 study Biology only.
(i) Represent this information on a Venn diagram.
(ii) How many pupils study all the subjects?
(iii) If a pupil is selected at random, what is the probability that he studies either Physics or Chemistry?
(i) The Venn diagram can be drawn as follows:
|Biology| |Physics| |Chemistry|
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| | PB | | PC | | BC |
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| B | | P | | C |
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(ii) From the Venn diagram, we can see that only 1 pupil studies all three subjects.
(iii) To find the probability that a pupil studies either Physics or Chemistry, we need to add up the number of pupils in the Physics only, Chemistry only, and Physics and Chemistry categories.
From the Venn diagram, we can see that:
- The number of pupils in the Physics only category is 2.
- The number of pupils in the Chemistry only category is 3.
- The number of pupils in the Physics and Chemistry category is 10.
So, the total number of pupils studying either Physics or Chemistry is 2 + 3 + 10 = 15.
Therefore, the probability that a randomly selected pupil studies either Physics or Chemistry is 15/40 = 3/8.