Probability Distributions (CIE A Level Maths: Probability & Statistics 1)

Exam Questions

3 hours30 questions

3 marks

The discrete random variable, X, is defined as the number of sixes obtained from rolling two fair dice.

(i)

Find the probability of obtaining two sixes from rolling two fair dice.

(ii)

Complete the following probability distribution table for X:

$x$	0	1	2
$P (X = x)$	$\frac{25}{36}$

How did you do?

2 marks

Use the table, or otherwise, to find the probability of obtaining at least one six from rolling two fair dice.

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$x$	2	4	6	8	10
$P (X = x)$	$\frac{2}{5}$	$\frac{1}{10}$	$\frac{1}{5}$	$p$	$\frac{1}{10}$

$x$	1	2	3	4	5
$P (X = x)$	$\frac{5}{12}$	$\frac{2}{12}$	$\frac{1}{12}$	$\frac{3}{12}$	$\frac{1}{12}$

$x$	1	2	3	4	5
$P (X = x)$	$\frac{1}{5}$	$\frac{1}{10}$	$p$	$p$	$q$

x	0	1	2	3	4
P(X = x)	$\frac{5}{24}$	$\frac{1}{3}$	$\frac{1}{4}$	$\frac{1}{12}$	$\frac{1}{8}$

$x$	2	3	5	7	11
$P (X = x)$	$\frac{1}{4}$	$\frac{1}{3}$	$p$	$\frac{1}{6}$	$\frac{1}{12}$

$x$	$- 2$	$0$	$2$	$4$	$6$
$P (X = x)$	$p$	$\frac{1}{2}$	$q$	$\frac{1}{15}$	$q$

number on sector	0	1	1	2	3	5
probability	$\frac{6}{20}$	$p$	$\frac{3}{20}$	$\frac{5}{20}$	$\frac{3}{20}$	$\frac{1}{20}$

$x$	$- 1$	$1$	$2$
$P (X = x)$	$\frac{5}{12}$	$p$	$\frac{1}{4}$

$x$	$- 2$	$0$	$2$	$4$	$6$
$P (X = x)$	$p$	$\frac{2}{15}$	$\frac{1}{4}$	$\frac{2}{15}$	$p$

$y$	-2	0	1	2	3	4
$P (Y = y)$

$y$	$- 4$	$0$	4	8
$P (Y = y)$		$\frac{2}{15}$