Edexcel IGCSE Math A Higher 6.3 Probability

[Maximum number: 4]

A biased spinner has three sections each of a different colour.
The table shows the probability that, when the spinner is spun once, it will land on blue or on orange or on white.

Table for Question 1 — Edexcel IGCSE Math A Higher

(a)

Work out the value of x

x=

The spinner is spun 250 times.

[ 2 ]

Remaining probability:
1-0.58=0.42

Since the other probabilities are 2x and x:
0.58+2x+x=13x=0.42

Final answer:
x=0.14

Equivalent answers accepted, for example $14\%$ or $\frac{7}{50}$ .

(b)

Work out an estimate for the number of times the spinner will land on blue.

[ 2 ]

Estimate:
$250\times0.58=145$

Final answer:
145

M1 for $250\times0.58$ or equivalent.

[Maximum number: 5]

Grace is going to spin the arrow on the spinner once.

The table below gives the probabilities that the spinner will land on red or on blue or on green.
The probability that the spinner will land on orange is 3 times the probability that the spinner will land on pink.

Figure for Question 2 — Edexcel IGCSE Math A Higher

Table for Question 2 — Edexcel IGCSE Math A Higher

(a)

Work out the probability that the spinner will land on orange.

[ 3 ]

Working:
1-(0.2+0.12+0.08)=0.6 $0.6\times\frac34=0.45$

Final answer:
0.45

M1 for a correct calculation or equation for the remaining probability. M1 for finding $\frac34$ of the remaining probability. A1 for 0.45, $\frac{9}{20}$ , $45\%$ , or $\frac{0.45}{1}$ .

(b)

Grace spins the arrow on the spinner 150 times.

Work out an estimate for the number of times the spinner lands on blue.

[ 2 ]

Working:
$0.12\times150=18$

Final answer:
18

M1 for a correct calculation for the number of times the spinner lands on blue. A1 for 18. An answer of $\frac{18}{150}$ scores M1A0 because it is a probability, not a number of times.

[Maximum number: 2]

100 farmers are asked if they have goats (G), sheep (S) or chickens (C) on their farms.
Of these farmers
31 have sheep
53 have chickens
6 have goats, sheep and chickens
11 have sheep and goats
17 have sheep and chickens
18 have goats and chickens
20 do not have any goats, sheep or chickens

Find the probability that this farmer also has goats.

Final answer:
$\frac{18}{53}$

Accept $0.33\ldots$ or $33.96\ldots\%$ . Follow through from the candidate's Venn diagram.

[Maximum number: 2]

A biased spinner has three sections each of a different colour.
The table shows the probability that, when the spinner is spun once, it will land on blue or on orange or on white.

Table for Question 4 — Edexcel IGCSE Math A Higher

Work out the value of x

x=

The spinner is spun 250 times.

Remaining probability:
1-0.58=0.42

Since the other probabilities are 2x and x:
0.58+2x+x=13x=0.42

Final answer:
x=0.14

Equivalent answers accepted, for example $14\%$ or $\frac{7}{50}$ .

[Maximum number: 3]

Grace is going to spin the arrow on the spinner once.

The table below gives the probabilities that the spinner will land on red or on blue or on green.
The probability that the spinner will land on orange is 3 times the probability that the spinner will land on pink.

Figure for Question 5 — Edexcel IGCSE Math A Higher

Table for Question 5 — Edexcel IGCSE Math A Higher

Work out the probability that the spinner will land on orange.

Working:
1-(0.2+0.12+0.08)=0.6 $0.6\times\frac34=0.45$

Final answer:
0.45

M1 for a correct calculation or equation for the remaining probability. M1 for finding $\frac34$ of the remaining probability. A1 for 0.45, $\frac{9}{20}$ , $45\%$ , or $\frac{0.45}{1}$ .

[Maximum number: 2]

The table shows information about the weights, in kilograms, of 40 babies.

Table for Question 6 — Edexcel IGCSE Math A Higher

Find the probability that this baby has a weight of more than 5 kg .

$\frac{2}{40}+\frac{1}{40}=\frac{3}{40}$

Final answer:
$\frac{3}{40}$

Equivalent:
0.075

[Maximum number: 3]

Ciara throws four fair six-sided dice.
The faces of each dice are labelled with the numbers 1,2,3,4,5,6
Work out the probability that at least one of the dice lands on an even number.

Probability no dice lands on an even number:
$\left(\frac12\right)^4=\frac{1}{16}$

Therefore:
$1-\left(\frac12\right)^4=\frac{15}{16}$

Final answer:
$\frac{15}{16}$

Equivalent decimals accepted, for example 0.9375.

[Maximum number: 1]

Here is a biased spinner.

Figure for Question 8 — Edexcel IGCSE Math A Higher

When the spinner is spun once, the probabilities that it lands on red or on yellow or on green are given in the table.

Table for Question 8 — Edexcel IGCSE Math A Higher

Work out the probability that the spinner lands on red or on yellow.

0.45

1

B1 oe eg $\frac{9}{20}, \frac{45}{100}, 45 \%$

[Maximum number: 2]

Grace is going to spin the arrow on the spinner once.

The table below gives the probabilities that the spinner will land on red or on blue or on green.
The probability that the spinner will land on orange is 3 times the probability that the spinner will land on pink.

Figure for Question 9 — Edexcel IGCSE Math A Higher

Table for Question 9 — Edexcel IGCSE Math A Higher

Grace spins the arrow on the spinner 150 times.

Work out an estimate for the number of times the spinner lands on blue.

Working:
$0.12\times150=18$

Final answer:
18

M1 for a correct calculation for the number of times the spinner lands on blue. A1 for 18. An answer of $\frac{18}{150}$ scores M1A0 because it is a probability, not a number of times.

[Maximum number: 2]

Emilie takes part in two races.
The probability that she wins the first race is 0.7
The probability that she wins the second race is 0.4
The outcomes of the two races are independent.

Complete the probability tree diagram.

First race

Second race

Figure for Question 10 — Edexcel IGCSE Math A Higher

First race missing probability:
0.3
Second race branch probabilities:
$0.6,\quad 0.4,\quad 0.6$
B1 for the first race branch, B1 for the second race branches.

[Maximum number: 3]

Emilie takes part in two races.
The probability that she wins the first race is 0.7
The probability that she wins the second race is 0.4
The outcomes of the two races are independent.

Work out the probability that Emilie wins exactly one of the two races.

Emilie is going to take part in a third race.
If she wins both of the first two races, the probability that she will win the third race is 0.6 If she wins exactly one of the first two races, the probability that she will win the third race is 0.3

Exactly one win:
$0.7\times0.6+0.3\times0.4 = 0.42+0.12 = 0.54$
Final answer:
0.54
Equivalent answer $\frac{27}{50}$ accepted.

[Maximum number: 5]

Here are 9 cards. Each card has either a number on it or a letter on it.

Figure for Question 12 — Edexcel IGCSE Math A Higher

Tomas is playing a game.
Tomas takes at random one of the cards and keeps it.
Tomas then takes at random another card and keeps it.

(a)

Work out the probability that each of the two cards has a number on it.

[ 2 ]

$\frac29\times\frac18=\frac{2}{72}=\frac1{36}$
Final answer:
$\frac1{36}$
Equivalent decimal to at least 2 significant figures accepted.

(b)

Work out the probability that there will be one card with a number on it and one card with a letter on it.

[ 3 ]

One number and one letter:
$\frac29\times\frac78+\frac79\times\frac28$ $=\frac{14}{72}+\frac{14}{72} =\frac7{18}$
Final answer:
$\frac7{18}$
Equivalent decimal to at least 2 significant figures accepted.

[Maximum number: 3]

Emilie takes part in two races.
The probability that she wins the first race is 0.7
The probability that she wins the second race is 0.4
The outcomes of the two races are independent.

Work out the probability that Emilie will win exactly two of the three races.

Exactly two wins in three races:
$0.7\times0.4\times(1-0.6)=0.112$ $0.54\times0.3=0.162$ 0.112+0.162=0.274
Final answer:
0.274
Equivalent answer $\frac{137}{500}$ accepted.

Edexcel IGCSE Math A Higher 6.3 Probability Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (b)

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question (a)

Question (b)

Question 13