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In Melbourne, a local community event offers two choices for a free gift: a reusable coffee cup or a tote bag. Each participant can choose one item, and the event organisers record the choices by gender.
Out of 120 participants, 70 are female and 50 are male. Among the females, 40 chose the coffee cup and 30 chose the tote bag.
Among the males, 25 chose the coffee cup and 25 chose the tote bag. Using a two-way table, determine the exact probability that a randomly selected participant is male AND chose the tote bag.
Express your answer as a simplified fraction.
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Worked solution
- Identify the total number of participants and the specific group of interest. The total participants are 120. The group of interest is male participants who chose the tote bag.
- Construct a two-way table using the given data. The rows represent gender (female, male), and the columns represent gift choice (coffee cup, tote bag). Fill in the values: 40 females chose coffee cup, 30 chose tote bag; 25 males chose coffee cup, 25 chose tote bag.
- Verify the total number of participants by summing all entries in the table: 40 (female, coffee cup) + 30 (female, tote bag) + 25 (male, coffee cup) + 25 (male, tote bag) = 120. This matches the given total, confirming data consistency.
- Locate the cell for 'male' and 'tote bag' in the two-way table. The value is 25, meaning 25 participants are male and chose the tote bag.
- Calculate the probability as the ratio of the number of favourable outcomes to the total number of outcomes. Probability = (number of males who chose tote bag) / (total participants) = 25 / 120.
- Simplify the fraction 25/120. Both numerator and denominator are divisible by 5: 25 ÷ 5 = 5, 120 ÷ 5 = 24. The simplified fraction is 5/24.
- Check the simplification: 5 and 24 have no common factors other than 1, so 5/24 is in simplest form. The final probability is 5/24.
Reference answer: 5/24
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