PK 2015 Q8
8. The picture shows the same die in three different positions. When the die is rolled, what is the probability of rolling a ‘YES’ ?
- A \(\dfrac{1}{3}\)
- B \(\dfrac{1}{2}\)
- C \(\dfrac{5}{9}\)
- D \(\dfrac{2}{3}\)
- E \(\dfrac{5}{6}\)
Pink Kangaroo 2015, Question 8. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B \(\dfrac{1}{2}\)
We will show that the word “YES” appears exactly three times, giving the probability 3/6 or 1/2. Firstly note that “YES” appears twice on the second die. The third die also shows “YES” and this cannot be the same as either “YES” on the second die: Under the first “YES” is “MAYBE”, but on the third die the word “NO” appears below it; to the left of the second “YES” is “MAYBE”, but to the left of the “YES” on the third die is “NO”. Hence “YES” appears at least three times. However, it appears at most three times because there are two occurrences of “NO” shown in the third die, and one “MAYBE” in the second die. The first die has not been used in the above argument, but is consistent with the faces showing “YES” three times, “NO” twice, and “MAYBE” once.
Solution © UK Mathematics Trust, from the PK 2015 solutions.