Worksheets · Foundation and Higher

Independent and dependent event trees

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 4 marks
The probability that it rains on any day is 0.3. Assume the weather on Monday and on Tuesday is independent.
(a) Work out the probability that it rains on both days. (2)
(b) Work out the probability that it rains on neither day. (2)
Question 2Non-calculator · 4 marks
A bag contains 5 red counters and 3 blue counters. Two counters are taken at random, one after the other, without replacement.
(a) Work out the probability that both counters are the same colour. (4)
Question 3Non-calculator · 3 marks
A box contains 4 green balls and 6 yellow balls. Three balls are taken at random without replacement.
(a) Work out the probability that at least one of the balls is green. (3)

Answers and marks

(a) 0.09

(b) 0.49

(a) $\frac{13}{28}$

(a) $\frac{5}{6}$

P1 Using $1 - P(\text{no green})$ (or listing all seven green-containing cases).
P1 $\frac{6}{10} \times \frac{5}{9} \times \frac{4}{8}$ .
A1 $\frac{5}{6}$ or equivalent.

Independent and dependent event trees

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