| Date | None Specimen | Marks available | 3 | Reference code | SPNone.1.hl.TZ0.3 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Find | Question number | 3 | Adapted from | N/A |
Question
A bag contains three balls numbered 1, 2 and 3 respectively. Bill selects one of these balls at random and he notes the number on the selected ball. He then tosses that number of fair coins.
Calculate the probability that no head is obtained.
[3]
a.
Given that no head is obtained, find the probability that he tossed two coins.
[3]
b.
Markscheme
P(no heads from n coins tossed) = \({0.5^n}\) (A1)
P(no head) = \(\frac{1}{3} \times \frac{1}{2} + \frac{1}{3} \times \frac{1}{4} + \frac{1}{3} \times \frac{1}{8}\) M1
= \(\frac{7}{{24}}\) A1
[3 marks]
a.
\({\text{P(2 | no heads)}} = \frac{{{\text{P(2 coins and no heads)}}}}{{{\text{P(no heads)}}}}\) M1
\( = \frac{{\frac{1}{{12}}}}{{\frac{7}{{24}}}}\) A1
\( = \frac{2}{7}\) A1
[3 marks]
b.
Examiners report
[N/A]
a.
[N/A]
b.
