Identifies proportion of the intersection of the 1 C two sets (c) 1 C Identifies proportion of students not passing both tests. Uses correct rule to test for independence 1 C (d) Selects correct probabilities to substitute into 1 C So events not independent the rule Question 10 (3 marks) Task Solution Behaviours Marks (S/C) = 1 (0.05+0.16+0.44+0.23+0.07) – (a) Identifies probability sums to 1 1 S = 0.05 =0.957 Applies the conditional probability 1 C (b) formula Evaluates correctly 1 S Question 11 (6 marks) Task Solution Marks (S/C) M K and If are mutually exclusive then Behaviours (a) C Applies the formula for conditional probability 1 C Calculates 1 S Uses the fact that the intersection is empty if sets are mutually exclusive 1 If sets are independent, then Behaviours (b) S Applies rule for independence 1 C Expands and substitutes the value for 1 C Solves the equation for 1
(c) Identifies proportion of the intersection of the two sets Identifies proportion of students not passing both tests. 1 1 C C (d) So events not independent Uses correct rule to test for independence Selects correct probabilities to substitute into the rule 1 1 C C Question 10 (3 marks) Solution Behaviours Marks Task (S/C) (a) = 1 – (0.05+0.16+0.44+0.23+0.07) = 0.05 Identifies probability sums to 1 1 S (b) =0.957 Applies the conditional probability formula Evaluates correctly 1 1 C S Question 11 (6 marks) Solution Marks Task (S/C) (a) If M and K are mutually exclusive then Behaviours Applies the formula for conditional probability Calculates Uses the fact that the intersection is empty if sets are mutually exclusive 1 1 1 C C S (b) If sets are independent, then Behaviours Applies rule for independence Expands and substitutes the value for Solves the equation for 1 1 1 S C C