IB Mathematics SL 4.11 Conditional Probabilities AA SL Paper 2- Exam Style Questions- New Syllabus
▶️ Answer/Explanation
a) (i) 
Note: Award A1 for a correctly labelled tree diagram and A1 for correct probabilities. [2]
(ii) \( P(F) = 0.6 \times 0.02 + 0.4 \times 0.01 \)
\( = 0.012 + 0.004 = 0.016 \) [2]
(iii) \( P(A|F) = \frac{P(A \cap F)}{P(F)} \)
\( = \frac{0.6 \times 0.02}{0.016} = \frac{0.012}{0.016} = 0.75 \) [2]
b) (i) METHOD 1:
\( P(X = 2) = \frac{^3C_2 \times ^4C_1}{^7C_3} \)
\( = \frac{12}{35} \) [2]
METHOD 2:
\( \frac{3}{7} \times \frac{2}{6} \times \frac{4}{5} \times 3 \)
\( = \frac{12}{35} \) [2]
(ii) 
Note: Award A1 if \( \frac{4}{35}, \frac{18}{35}, \) or \( \frac{1}{35} \) is obtained. [2]
(iii) \( E(X) = \sum x P(X = x) \)
\( E(X) = 0 \times \frac{4}{35} + 1 \times \frac{18}{35} + 2 \times \frac{12}{35} + 3 \times \frac{1}{35} \)
\( = \frac{45}{35} = \frac{9}{7} \) [2]