CAIE IGCSE Mathematics Extended E8.3 Probab…vents

Covered syllabus points

E8.3.1 Calculate the probability of combined events using, where appropriate:

[Maximum number: 5]

On any day the probability that it rains is $\frac{1}{3}$ .
When it rains the probability that Amira goes fishing is $\frac{3}{5}$ .
When it does not rain the probability that Amira goes fishing is $\frac{3}{4}$ .

(a)

Complete the tree diagram.

Figure for Question (a) — CAIE IGCSE Mathematics Extended

[ 2 ]

Figure for Answer to Question (a) — CAIE IGCSE Mathematics Extended

$\frac{2}{3},\frac{2}{5},\frac{3}{4},\frac{1}{4}$ oe

M1 for 2 or 3 correct.

(b)

Find the probability that on any day Amira goes fishing.

[ 3 ]

$\frac{7}{10}$ oe

M2 for $\frac13\times\frac35+$ their $\frac23\times$ their $\frac34$ .
M1 for one product.

[Maximum number: 3]

The histogram shows information about the masses of some coconuts.
The masses are classified into four categories A, B, C and D.

Figure for Question 2 — CAIE IGCSE Mathematics Extended

Two of the coconuts from those in category C and category D are chosen at random.

Find the probability that both are from category D.

$\frac{5}{39}$ oe

M2 for $\frac{10}{10+170 \times 0.1} \times \frac{9}{9+170 \times 0.1}$ oe or $\mathbf{M 1}$ for $\frac{10}{10+17}$ or $\frac{9}{10+16}$ or $\frac{9}{10+17}$ or $\frac{10}{10+16}$ oe seen

or $\frac{10}{k} \times \frac{9}{k-1}$ oe with k>10 and an integer or $\frac{m}{10+17} \times \frac{m-1}{10+16}$ oe with 0<m<27 and an integer

[Maximum number: 9]

Bag A

Bag B

Bag A contains 5 white balls and 3 black balls.
Bag B contains 3 white balls and 1 black ball.

(a)

Two balls are picked at random from bag B without replacement.

Find the probability that both balls are black.

[ 1 ]

(b)

The balls are replaced into bag B .

Kyle picks a ball at random from each bag.

[ 5 ]

(i)

Complete the tree diagram.

Figure for Question (i) — CAIE IGCSE Mathematics Extended

[ 2 ]

Figure for Answer to Question (i) — CAIE IGCSE Mathematics Extended

See completed tree diagram in answer image.

B1 for $\frac38$
or for $\frac34$ and $\frac14$ correctly placed on the same pair of branches

(ii)

Find the probability that the two balls are the same colour.

[ 3 ]

$\frac{18}{32}$ oe

M2 for $\frac58\times\frac34+\frac38\times\frac14$ oe
or M1 for one correct branch e.g. $\frac58\times\frac34$ or $\frac38\times\frac14$ oe

(c)

The balls are replaced into their bags.

Jo picks a ball at random from bag A and places it into bag B . She then picks a ball at random from bag B .

Find the probability that she picks a black ball from bag B.

[ 3 ]

$\frac{11}{40}$ oe

M2 for $\frac58\times\frac15+\frac38\times\frac25$ oe
or M1 for one product of the form $\frac58\times\frac{k}{5}$ or $\frac38\times\frac{k}{5}$ oe, k=1,2,3 or 4

All question bank results loaded

CAIE IGCSE Mathematics Extended E8.3 Probability of Combined Events Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question 3

Question (a)

Question (b)

Question (i)

Question (ii)

Question (c)