Date | May 2022 | Marks available | 2 | Reference code | 22M.1.SL.TZ2.2 |
Level | Standard Level | Paper | Paper 1 | Time zone | Time zone 2 |
Command term | Find | Question number | 2 | Adapted from | N/A |
Question
A group of 130 applicants applied for admission into either the Arts programme or the Sciences programme at a university. The outcomes of their applications are shown in the following table.
An applicant is chosen at random from this group. It is found that they were accepted into the programme of their choice.
Find the probability that a randomly chosen applicant from this group was accepted by the university.
Find the probability that the applicant applied for the Arts programme.
Two different applicants are chosen at random from the original group.
Find the probability that both applicants applied to the Arts programme.
Markscheme
(17+25130=) 42130 (2165, 0.323076…) A1
[1 mark]
(1717+25=) 1742 (0.404761…) A1A1
Note: Award A1 for correct numerator and A1 for correct denominator.
Award A1A0 for working of 17/130their answer to (a) if followed by an incorrect answer.
[2 marks]
41130×40129 A1M1
Note: Award A1 for two correct fractions seen, M1 for multiplying their fractions.
=164016770≈0.0978 (0.0977936…, 1641677) A1
[3 marks]
Examiners report
Candidates are reasonably proficient at calculating simple probabilities from a table.
Several candidates did not consider the condition, with some merely finding the probability of an applicant applying for Arts programme with no condition, some considering those who were accepted into Arts with no condition, and some finding the probability of being accepted into Arts given the condition that they applied for Arts.
Only a few candidates recognized dependent events, with most calculating as if the events were independent.