| (a) |
Explain what it means when we say that |
|
|
(i) Events A and B are
dependent. |
[1] |
|
(ii) Events A and B are
independent. |
[1] |
| (b) |
Let P(A), P(B), and P(A B)
be the probabilities of events A, B, and AB
happening. Give mathematical relationships relating each of these three probabilities (to
each other) for each of the following cases: |
|
|
(i) Events A and B are
dependent, |
[1] |
|
(ii) Events A and B are
independent, and |
[1] |
|
(iii) Events A and B are
mutually exclusive. |
[1] |
| (c) |
During winter in Scotland, Mr Nettawa
experiences difficulty in starting his two cars. The probability that the first car starts
is 0.6, and the probability that the second car starts is 0.4. There is the probability of
0.32 that both cars start. |
|
|
(i) Are these events (i.e. that each of the cars
starts) independent? Explain your answer. |
[2] |
|
(ii) What is the probability that the first car
starts but the second car doesn't? |
[1] |
|
(iii) What is the probability that the second
car starts but the first car doesn't? |
[1] |
|
(iv) What is the probability that at least car
starts? |
[1] |
|
(v) What is the probability that neither car
starts? |
[1] |
| (d) |
A computer manufacturer has undertaken a survey
of 100 businesses to determine which of the three types of external memory devices they
commonly use: CD, DVD or diskette. A total of 39 businesses uses DVD, whilst 73 businesses
made use of CD, 12 businesses used CD only, whilst 17 used only DVD, 42 businesses
used both CD and diskette, but not DVD. Only 4 businesses used all three devices; all of
the businesses used at least one of the devices. |
|
|
(i) Draw a Venn diagram to represent the results
of the survey. |
[5] |
|
(ii) How many businesses used CD and DVD, but
not diskettes? |
[1] |
|
(iii) How many businesses used DVD and
diskettes, but not CD? |
[1] |
|
(iv) What is the probability that a firm that
uses diskettes does not use CDs? |
[2] |