An experiment consists of tossing a coin and then rolling a fair six-sided die. What isthe probability of observing a head and a ‘six’?单项选择题
A
a. 1/12
B
b. 1/2
C
c. 1/35
D
d. 1/4

Question

An experiment consists of tossing a coin and then rolling a fair six-sided die. What isthe probability of observing a head and a ‘six’?

BlackTom AI · Accepted Answer

P(head) = 1/2 and P(rolling a six) = 1/6, so the combined probability is their product.

1. Relevant knowledge points and concepts
- Independent events: The coin toss and the die roll do not affect each other, so probabilities multiply.
- Probability of a single outcome in equally likely sample spaces: For a fair coin P(head) = 1/2; for a fair six-sided die P(6) = 1/6.
- Counting view: Total ordered outcomes = 2 (coin) × 6 (die) = 12 equally likely pairs.

2. Complete reasoning process step by step
- Step 1: Determine each marginal probability:
  P(head) = 1/2.
  P(6 on die) = 1/6.
- Step 2: Because the events are independent, use multiplication rule:
  P(head and 6) = P(head) × P(6).

3. Calculations with intermediate steps
- Multiply the fractions:
  P = (1/2) × (1/6)
    = 1/(2 × 6)
    = 1/12.

- Counting viewpoint: List ordered pairs (Coin,Die). There are 12 pairs; only (Head,6) satisfies the condition, so probability = 1/12.

4. Why the correct answer is correct
- Independence justifies multiplying probabilities. Both analytic (fraction multiplication) and combinatorial (1 favorable of 12 total) approaches give the same result 1/12, confirming consistency.

5. Why the other options are incorrect
- b. 1/2: This ignores the die outcome and is far too large; it would mean half the experiments produce both a head and a six, which is impossible here.
- c. 1/35: No natural way to get 1/35 from a 2×6 experiment; this is incorrect.
- d. 1/4: This would be (1/2)×(1/2) — treating the die as if it had two equally likely outcomes — which is wrong for a six-sided die.

6. Conclusion
The probability of observing a head and a six is 1/12, matching option a.

An experiment consists of tossing a coin and then rolling a fair six-sided die. What isthe probability of observing a head and a ‘six’?单项选择题

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