With reference to the Venn diagram below, $S$ is the universal set and $A$ and $B$ are non-emp

Question

With reference to the Venn diagram below, $S$ is the universal set and $A$ and $B$ are non-empty proper subsets of $S$. Explain whether $A$ and $B$ are independent, and write down the value of $\mathrm{P}(A|B)$.[2] A fair die has three sides numbered $2$, two sides numbered $1$ and one side numbered $0$. A game is played by throwing this fair die three times and the score, $X$, is the sum of the numbers obtained. Show that $\mathrm{P}(X=2) = \frac{7}{72}$.[2] The table shows an incomplete probability distribution of $X$. Find the missing probabilities, showing your workings clearly.[3] Probability distribution of X$x$$0$$1$$2$$3$$4$$5$$6$ $\mathrm{P}(X = x)$$\frac{1}{216}$$\frac{1}{36}$$\frac{7}{72}$$\frac{7}{24}$ The game is played $5$ times. Find the probability that exactly one of the games obtained a score of $0$ and exactly $2$ games obtained a score of more than $2$.[3]

Accepted Answer

(a)1 (b)(iii)0.00164

2025 SAJC P2 Q7

2025 SAJC P2 Q7