Two friends, Sensen and Cruz, are conducting an investigation on probability.

Sensen has a fair six-sided die with faces numbered \(1,\,\,2,\,\,2,\,\,4,\,\,4\) and \(4\). Cruz has a fair disc with one red side and one blue side.

The die and the disc are thrown at the same time.

Find the probability that the number shown on the die is \(1\) and the colour shown on the disc is blue;

Find the probability that the number shown on the die is \(1\) or the colour shown on the disc is blue;

Find the probability that the number shown on the die is even given that the colour shown on the disc is red.

\(\frac{1}{2} \times \frac{1}{6}\)        (M1)

\(\frac{1}{{12}}\,\,(0.0833,\,\,8.33\,\% ,\,\,0.08333...)\)        (A1)    (C2)

\(\frac{1}{2} + \left( {\frac{1}{2} \times \frac{1}{6}} \right)\)        (M1)

OR

\(\frac{1}{6} + \frac{1}{2} - \frac{1}{{12}}\,\)        (M1)

\(\frac{7}{{12}}\,\,(0.583,\,\,58.3\,\% ,\,\,0.58333...)\)        (A1)     (C2)

Note: Award (M1)(A0) for a correct attempt at a possibility/sample space diagram or tree diagram or \(\frac{1}{6} + \left( {\frac{5}{6} \times \frac{1}{2}} \right)\), leading to an incorrect answer.

\(\frac{1}{3} + \frac{1}{2}\)        (M1)

OR

\(\frac{{\frac{5}{6} \times \frac{1}{2}}}{{\frac{1}{2}}}\)        (M1)

\(\frac{5}{6}\,\,(0.833,\,\,83.3\,\% ,\,\,0.83333...)\)        (A1)     (C2)

Notes: Award (M1)(A0) for a correct attempt at a possibility/sample space diagram or tree diagram, leading to an incorrect answer.

Question 5: Probability.
Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.

Question 5: Probability.
Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.

Question 5: Probability.
Some candidates confused the probability of both events occurring with the probability that one or the other occurs. Many candidates were unable to find the conditional probability. Candidates should not answer a probability question with an answer that exceeds one. Only the very best candidates did very well on this question; many found this to be one of the most challenging questions in the paper.