| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2005 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Binomial Distribution |
| Type | Direct binomial probability calculation |
| Difficulty | Moderate -0.3 Part (i) is a straightforward binomial probability calculation with n=5, p=3/8, requiring only direct formula application. Part (ii) uses basic conditional probability P(A∩B)=P(A)P(B|A) with simple algebra. Part (iii) repeats the same method. This is a standard S1 question testing routine application of binomial distribution and conditional probability with no problem-solving insight required, making it slightly easier than average. |
| Spec | 2.03d Calculate conditional probability: from first principles2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities |
6 Louise and Marie play a series of tennis matches. It is given that, in any match, the probability that Louise wins the first two sets is $\frac { 3 } { 8 }$.\\
(i) Find the probability that, in 5 randomly chosen matches, Louise wins the first two sets in exactly 2 of the matches.
It is also given that Louise and Marie are equally likely to win the first set.\\
(ii) Show that P (Louise wins the second set, given that she won the first set) $= \frac { 3 } { 4 }$.\\
(iii) The probability that Marie wins the first two sets is $\frac { 1 } { 3 }$. Find
P(Marie wins the second set, given that she won the first set).
\hfill \mbox{\textit{OCR S1 2005 Q6 [7]}}