Edexcel IGCSE Math A 6.3.HC Conditional Probability in Combined Events

Practise selections without replacement by updating totals and combining ordered paths for required outcomes.

Exam points

update both the favourable count and total after each selection without replacement
multiply along ordered paths and add paths that satisfy the same required outcome
form and solve a probability equation when an initial colour count is unknown

[Maximum number: 5]

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

Figure for Question 6.3.HC Simple conditional probability when combining events question 1 — 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.

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6.3.HC Simple conditional probability when combining events question 1

Question (a)

Question (b)