Probability Distributions

1a

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

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1b

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

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

$x$	-2	-1	0	1	2
$P (X = x)$	$\frac{1}{5}$	$\frac{1}{5}$

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

Probability Distributions (Edexcel A Level Maths: Statistics): Exam Questions

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

$x$	$a$	$b$	$c$
$P (X = x)$	$\log_{36} a$	$\log_{36} b$	$\log_{36} c$

$d$	10	20	30	40	50
$P (D = d)$	$\frac{k}{10}$	$\frac{k}{20}$	$\frac{k}{30}$	$\frac{k}{40}$	$\frac{k}{50}$

x	0	1	2	3
P(X=x)

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

$r$	2	3
$P (R = r)$	$\frac{1}{4}$	$\frac{3}{4}$

$g$	1	4
$P (G = g)$	$\frac{2}{3}$	$\frac{1}{3}$