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Calculating Simple Probability

For equally likely outcomes, probability is the number of favourable outcomes divided by the total number of outcomes.

Favourable Over Total

When every outcome is equally likely: P (event) = \frac{number of favourable outcomes}{total number of outcomes} You can also write that as favourable \div total.

Example 1 — probability from a die

A standard die is rolled. Find P(rolling an even number). 1 Favourable outcomes: {2, 4, 6} — that is 3 outcomes 2 Total outcomes: 6 3 Divide: P (even) = \frac{3}{6} = \frac{1}{2} = 0.5 (or 3 \div 6 = 0.5) Answer: \frac{1}{2} or 0.5

Example 2 — probability from a bag

A bag has 4 red, 3 blue, and 2 green balls (9 balls in total). Find P(blue). 1 Favourable outcomes: 3 (the blue balls) 2 Total outcomes: 4 + 3 + 2 = 9 3 Divide: P (blue) = \frac{3}{9} = \frac{1}{3} (or 3 \div 9 \approx 0.333) Answer: \frac{1}{3} \approx 0.333

Example 3 — most likely letter

A letter is picked at random from the word BANANA. Which letter is most likely? 1 Letters: B, A, N, A, N, A — 6 letters in total. 2 Counts: A appears 3 times, N appears 2 times, B appears 1 time. 3 P (A) = \frac{3}{6} = \frac{1}{2} — the largest — so A is most likely. Always count frequencies before comparing options.

Example 4 — honour cards

One card is drawn from a standard 52 -card pack. An honour card is A, J, Q or K. Each of 4 suits has 4 honours, so there are 16 honours. P (honour) = \frac{16}{52} = \frac{4}{13}

Practice

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A letter is picked at random from BANANA. Which is most likely?

A bag has 5 red, 3 blue, and 2 yellow balls (10 total). Find P(yellow) as a decimal.

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