Probability Distributions | CIE AS Maths: Probability & Statistics 1 Topic Questions 2020

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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1a

1 mark

Three biased coins are tossed.

Write down all the possible outcomes when the three coins are tossed.

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1b

3 marks

A random variable, X, is defined as the number of heads when the three coins are tossed minus the number of tails.

Given that for each coin the probability of getting heads is $\frac{3}{5}$ ,

complete the following probability distribution table for X:

$x$
$P (X = x)$

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1a

1 mark

Three biased coins are tossed.

Write down all the possible outcomes when the three coins are tossed.

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1b

3 marks

A random variable, X , is defined as the number of heads when the three coins are tossed.

Given that for each coin the probability of getting heads is $\frac{2}{3}$ ,

complete the following probability distribution table for X:

x	0	1	2	3
P(X = x)

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1a

1 mark

Two biased coins are tossed and a fair spinner with three sectors numbered 1 to 3 is spun.

Write down all the possible outcomes when the two coins are tossed and the spinner is spun.

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1b

5 marks

A random variable, $X$ , is defined as the number of heads when the two coins are tossed multiplied by the number the spinner lands on when it is spun.

For each coin the probability of getting heads is $\frac{1}{3}$ .

Complete the following probability distribution table for $X$ :

$x$	0	1	2	3	4	6
$P (X = x)$

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

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

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

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

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

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

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

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

CIE AS Maths: Probability & Statistics 1

Topic Questions

3.1 Probability Distributions