| Date | May 2012 | Marks available | 1 | Reference code | 12M.1.hl.TZ2.3 |
| Level | HL only | Paper | 1 | Time zone | TZ2 |
| Command term | Draw | Question number | 3 | Adapted from | N/A |
Question
On a particular day, the probability that it rains is \(\frac{2}{5}\) . The probability that the “Tigers” soccer team wins on a day when it rains is \(\frac{2}{7}\) and the probability that they win on a day when it does not rain is \(\frac{4}{7}\).
Draw a tree diagram to represent these events and their outcomes.
What is the probability that the “Tigers” soccer team wins?
Given that the “Tigers” soccer team won, what is the probability that it rained on that day?
Markscheme
let R be “it rains” and W be “the ‘Tigers’ soccer team win”
A1
[1 mark]
\({\text{P}}(W) = \frac{2}{5} \times \frac{2}{7} + \frac{3}{5} \times \frac{4}{7}\) (M1)
\( = \frac{{16}}{{35}}\) A1
[2 marks]
\({\text{P}}(R\left| W \right.) = \frac{{\frac{2}{5} \times \frac{2}{7}}}{{\frac{{16}}{{35}}}}\) (M1)
\( = \frac{1}{4}\) A1
[2 marks]
Examiners report
This question was well answered in general.
This question was well answered in general.
This question was well answered in general.
