List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card from a set of 6 cards numbered 1 through 6.
Answer: S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}; n(S) = 2 × 6 = 12.
Step-by-step solution
Idea: Each outcome is a pair: the coin face (H or T) with the card number (1 to 6). Pair each face with every number.
- Coin: H or T. Card: 1, 2, 3, 4, 5 or 6. Number of pairs = 2 × 6 = 12.½ mark
- With heads: H1, H2, H3, H4, H5, H6. With tails: T1, T2, T3, T4, T5, T6.1 mark
- S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, n(S) = 12.½ mark
S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}, which has 12 elements.
Check: 6 elements with H + 6 with T = 12 ✓; every pair appears once.
Answer to write in the exam
n(S) = 2 × 6 = 12
∴ S = {H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6}
Common mistakes that cost marks
- Writing {H, T, 1, 2, 3, 4, 5, 6} (8 items). Both actions happen together, so each element is a pair like H3.
- Listing only the heads pairs and forgetting the tails pairs.
- Writing H3 and 3H as two different elements. They describe the same result, so list it once.
How this can come in the exam
MCQ (1 mark)
A coin is tossed and a card is drawn from 6 cards numbered 1 to 6. The probability of getting tails and an even number is
- 112
- 16
- 14
- 12
Show answer
(C) 14
Favourable: T2, T4, T6: 312 = 14.
Short answer (2 marks)
A coin is tossed and a spinner with four equal sectors marked A, B, C, D is spun at the same time. List the sample space and find the probability of heads with a vowel.
Show answer
S = {HA, HB, HC, HD, TA, TB, TC, TD}, n(S) = 8. Heads with a vowel: HA only. P = 18.Try one yourself
A coin is tossed and a card is drawn from 3 cards marked X, Y, Z. List the sample space.
Show answer
{HX, HY, HZ, TX, TY, TZ}: 6 elements.
More questions like this
- Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for this experiment? Why do the other lists fail to qualify as a sample space?
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