The following ordered pairs of numbers
$\left(x,y\right)$ were
obtained in an experiment:

$$\left(1,2\right),\left(2,4\right),\left(3,6\right),\left(3,7\right).$$

Without performing calculations, what is the best description of the size of the
correlation coefficient of the data ?
Exactly one option must be correct)
*Choice (a) is correct!*

By inspection, we see that the correlation coefficient must be positive but the
magnitude of the correlation coefficient can never be greater than 1.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

We are told that in a random experiment there are five possible outcomes. Which of
the following statements is true ?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is correct!*

In a random experiment the outcomes are independent so the first two statements are
incorrect. We do not have enough information to comment on the probability of each
outcome, so the fourth statement is incorrect.

*Choice (d) is incorrect*

A coin is tossed 6 times. What is the probability of exactly 2 heads occurring in the 6
tosses.
Exactly one option must be correct)

*Choice (a) is correct!*

The two heads can occur in any of the six tosses, so there are
$\left(\begin{array}{c}\hfill 6\hfill \\ \hfill 2\hfill \end{array}\right)$ arrangements, with
a probability of ${\left(\frac{1}{2}\right)}^{6}$
for each arrangement.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

A coin is tossed 6 times. What is the probability of getting 2 heads, followed by 4
tails ?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is correct!*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

A coin is tossed and a fair six sided die is thrown. How many possible outcomes are
there ?
Exactly one option must be correct)

*Choice (a) is correct!*

Each die face can come up with a head or a tail. The number of possible outcomes is
therefore $6+6=12$.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

Two fair dice are tossed. How many possible outcomes are there ?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is correct!*

*Choice (d) is incorrect*

Two fair dice are thrown. What is the probability of the sum of 10 being obtained for
the two uppermost faces ?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is correct!*

The possible pairs of faces are $\left(4,6\right)$,
$\left(5,5\right)$ and
$\left(6,4\right).$
That is, 3 out of a possible 36. The probability is therefore
$\frac{3}{36}=\frac{1}{12}$.

What is the value of $\left(\begin{array}{c}\hfill n\hfill \\ \hfill r\hfill \end{array}\right)$
with $n=7$
and $r=2$
?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is correct!*

$\left(\begin{array}{c}\hfill n\hfill \\ \hfill r\hfill \end{array}\right)=\frac{n\phantom{\rule{0.3em}{0ex}}!}{r\phantom{\rule{0.3em}{0ex}}!\left(n-r\right)\phantom{\rule{0.3em}{0ex}}!}=\frac{7\phantom{\rule{0.3em}{0ex}}!}{2\phantom{\rule{0.3em}{0ex}}!\phantom{\rule{0.3em}{0ex}}5\phantom{\rule{0.3em}{0ex}}!}=\frac{7\times 6}{2}=21\phantom{\rule{0.3em}{0ex}}.$

*Choice (d) is incorrect*

A fair coin is tossed twice. What is the probability of obtaining a head and a tail
?
Exactly one option must be correct)

*Choice (a) is correct!*

The two possible outcomes are HT and TH, each of which has probability
$\frac{1}{4}$. The probability of a head
and a tail is therefore $\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$.

*Choice (b) is incorrect*

*Choice (c) is incorrect*

*Choice (d) is incorrect*

A coin is tossed until two heads occur on successive throws. The number of tosses is
described by which of the following ?
Exactly one option must be correct)

*Choice (a) is incorrect*

*Choice (b) is incorrect*

*Choice (c) is correct!*

*Choice (d) is incorrect*