A fair die and a biased die are thrown. The events $A$, $B$ and $C$ are defined as follows: $A$: the

Question

A fair die and a biased die are thrown. The events $A$, $B$ and $C$ are defined as follows:

$A$: the score on the fair die is odd

$B$: the score on the biased die is even

$C$: the sum of the two scores is odd.

The biased die has probabilities given by $\mathrm{P}$ (score is $r$) $=\frac{r}{21}$ where $r=1,2,3,4,5,6$. Identify two events that are independent. Support your answers with a reason.

Find $\mathrm{P}\left( A \right)$, $\mathrm{P}\left( B \right)$ and $\mathrm{P}\left( C \right)$.
Find $\mathrm{P}\left( A\cap C \right)$ and $\mathrm{P}\left( A|C \right)$.

Accepted Answer

(i) $P(A)=\dfrac12$, $P(B)=\dfrac47$, $P(C)=\dfrac12$ (ii) $P(A\cap C)=\dfrac27$, $P(A\mid C)=\dfrac47$ Independent pairs: $A$ and $B$, and $B$ and $C$

Probability Q1: A Fair and a Biased Die are Thrown

Probability Q1: A Fair and a Biased Die are Thrown

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