A letter is picked at random from the word ‘PROBABILITY’. What is the probability of picking the letter B?
Step-by-step solution
To find: P(B)
Idea: Each of the letters in the word (counting repeats separately) is equally likely to be picked. Count all the letters and count the Bs.
- Write out the letters: P, R, O, B, A, B, I, L, I, T, Y.½ mark
- Number of all possible outcomes = 11 (the number of letters in the word PROBABILITY).½ mark
- Number of favourable outcomes = 2 (there are 2 Bs in the word PROBABILITY).½ mark
- P(picking the letter B) = 211 = 0.1818… ≈ 0.182 or 18.2%.½ mark
Check: Letter counts: P 1, R 1, O 1, B 2, A 1, I 2, L 1, T 1, Y 1. Total 1 + 1 + 1 + 2 + 1 + 2 + 1 + 1 + 1 = 11 ✓.
Answer to write in the exam
Letters: P, R, O, B, A, B, I, L, I, T, Y
Number of possible outcomes = 11
Number of favourable outcomes = 2 (two Bs)
∴ P(picking the letter B) = 211 = 0.1818… ≈ 0.182 or 18.2%
Common mistakes that cost marks
- Counting only the different letters (P, R, O, B, A, I, L, T, Y = 9) and writing 29. Each letter of the word is a separate outcome, so the total is 11.
- Counting only one B and writing 111. B appears twice.
- Rounding 0.1818… to 0.181 instead of 0.182.
How this can come in the exam
A letter is chosen at random from the word ‘MISSISSIPPI’. The probability that it is S is
- 111
- 411
- 14
- 47
Show answer
(B) 411
11 letters; S appears 4 times. P = 411.
A letter is picked at random from the word ‘ELEPHANT’. Find the probability that it is (a) E, (b) a vowel.
Show answer
8 letters: E, L, E, P, H, A, N, T. (a) Two Es: P(E) = 28 = 14. (b) Vowels E, E, A: P = 38.Try one yourself
A letter is picked at random from the word ‘BANANA’. What is the probability of picking A?
Show answer
6 letters, 3 of them A: P(A) = 36 = 12 = 0.5.
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