How to Take This Test
The 25 questions cover the whole chapter in the mix a Tier 2 paper uses: two dice and coins, a number or a letter picked at random, cards, balls and tickets, and two or three people or events put together. They come in no fixed order, as in the exam, so decide quickly whether a question needs a list of outcomes, , a complement or a product. Set a timer for 25 minutes, about a minute a question, and open the explanations only after the time is over.
Marking (Tier 2). +3 for a right answer, for a wrong one, 0 for a question left blank; the maximum is 75. With 20 right, 3 wrong and 2 left blank the score is .
| Score (out of 75) | What to do next |
|---|---|
| 60 or more | You are ready for the probability questions of the exam. Keep your speed with the PYQ Practice Set. |
| 45 to 59 | The methods are in place. Sort the questions you missed by their tag and redo that section's quiz: Basics of Probability, Coins and Dice, Cards, Balls and Bags or Combined Events. |
| 30 to 44 | Most marks are lost in counting. Go through Shortcuts & Speed Methods again, redo Practice Sets 2 and 3, and sit this test again a few days later. |
| Below 30 | Go back to Basics of Probability and Coins and Dice, write out the outcomes by hand for every question, and finish Practice Set 1 before you time yourself again. |
On guessing: under +3 and , a blind pick among four options gains nothing on average, because just balances ; a pick between two options gains a mark on average. Probability options are often easy to thin out: no probability is more than 1, the chance of both events cannot be bigger than the chance of either one, and the chance of at least one cannot be smaller.