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12 There are 30 students in Mr Lear’s class - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 2
Question 12
12 There are 30 students in Mr Lear’s class. 16 of the students are boys. Two students from the class are chosen at random. Mr Lear draws this probability tree dia... show full transcript
Worked Solution & Example Answer:12 There are 30 students in Mr Lear’s class - Edexcel - GCSE Maths - Question 12 - 2017 - Paper 2
Step 1
Write down one thing that is wrong with the probabilities in the probability tree diagram.
Answer
One issue with the probabilities in the probability tree diagram is that the sum of the probabilities for the '1st student' does not equal 1. The probability of selecting a boy is represented as 15/30 and that of selecting a girl is 16/30. These probabilities should actually add up to 1 but they don’t:
eq 1 $$Step 2
Is Mr Slater right?
Answer
No, Mr Slater is not correct. The probabilities for events that are independent (like Owen scoring a goal and Wasim scoring a goal) should be multiplied together, not added. To find the probability that both boys will score a goal, you multiply the individual probabilities:
Thus, the valid probability is 0.1, not 0.4 + 0.25.