Toss a paper cup into the air 100 times. After each toss record whether the cup lands on its bottom, upside down on its top or on its side (See the figure). Assign probabilities to the outcomes by using experimental probability.

Step-by-step solution

Idea: The three outcomes are not equally likely (a cup is not symmetrical like a coin), so we cannot just say 13 each. We must experiment and use relative frequency: P(outcome) = Number of times it happened100.

1. Make a tally table with three rows (bottom, top, side) and put a tally mark after each of the 100 tosses.½ mark
2. Sample results (one class’s experiment; yours will be different):
   bottom: 12 times; top (upside down): 23 times; side: 65 times. Check: 12 + 23 + 65 = 100.½ mark
3. Experimental probability = Number of times the outcome occurredTotal number of tosses:
   P(bottom) = 12100 = 0.12
   P(top) = 23100 = 0.23
   P(side) = 65100 = 0.651½ marks
4. Check and interpret: 0.12 + 0.23 + 0.65 = 1. Landing on its side is the most likely outcome and landing on its bottom the least likely. The outcomes are clearly not equally likely, which is why the probabilities had to be found by experiment.½ mark

Check: The three counts must add up to 100 and the three probabilities to 1. If your side count is far less than half, check that the cup was tossed high and allowed to fall freely each time.

Answer to write in the exam

Common mistakes that cost marks

• Assigning 13 to each outcome. The outcomes are not equally likely, so theoretical reasoning does not work here; use the experiment.
• Dividing by 3 (the number of outcomes) instead of by 100 (the number of tosses).
• Not checking that the counts add up to 100. A missed or double-counted toss makes every probability wrong.

How this can come in the exam

Try one yourself

A paper cup was tossed 80 times: bottom 10, top 18, side 52. Assign experimental probabilities to the three outcomes.

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