A fair six-sided die is rolled. Find the probability of getting a 4.
\( \dfrac{1}{6} \).
Probability
10 exam-style questions on single events, tree diagrams, Venn diagrams and combined probability.
3 Easy 4 Medium 3 Hard
A bag contains 3 red and 5 blue balls. One is picked at random. Find P(red).
\( \dfrac{3}{8} \).
P(rain) \( = 0.3 \). Find P(not rain).
\( 1 - 0.3 = 0.7 \).
Two fair coins are flipped. Find the probability of getting two heads.
\( \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4} \).
A spinner has sections: 1, 2, 2, 3, 3, 3. Find P(getting a 3).
\( \dfrac{3}{6} = \dfrac{1}{2} \).
P(A) \( = 0.4 \), P(B) \( = 0.5 \). A and B are independent. Find P(A and B).
\( 0.4 \times 0.5 = 0.2 \).
From a pack of 52 cards, one is drawn. Find P(heart or ace). Careful of overlap.
Hearts: 13, Aces: 4, Ace of hearts counted twice: \( \dfrac{13+4-1}{52} = \dfrac{16}{52} = \dfrac{4}{13} \).
A bag has 4 red and 6 blue balls. Two are drawn without replacement. Find P(both red).
\( \dfrac{4}{10} \times \dfrac{3}{9} = \dfrac{12}{90} = \dfrac{2}{15} \).
P(A) \( = 0.6 \), P(B) \( = 0.5 \), P(A and B) \( = 0.3 \). Find P(A or B).
\( P(A \cup B) = 0.6 + 0.5 - 0.3 = 0.8 \).
A bag has 5 green and 3 yellow counters. Two are taken at random without replacement. Find the probability that they are different colours.
P(GY) \( = \dfrac{5}{8} \times \dfrac{3}{7} = \dfrac{15}{56} \). P(YG) \( = \dfrac{3}{8} \times \dfrac{5}{7} = \dfrac{15}{56} \). Total \( = \dfrac{30}{56} = \dfrac{15}{28} \).