Praxis Core Academic Skills for Educators: Mathematics (5733)Statistics and ProbabilityMedium
A game involves spinning a fair 4-sided spinner numbered 1, 2, 3, 4, and flipping a fair coin. What is the probability of spinning an odd number AND flipping a tails?
- A1/2
- B1/8
- C1/4
- D3/8
Show answer & explanationAnswer & explanation
Correct answer: C. 1/4
The probability of spinning an odd number (1 or 3) on a 4-sided spinner is 2/4 = 1/2. The probability of flipping a tails on a fair coin is 1/2. Since these are independent events, the probability of both occurring is P(odd) * P(tails) = (1/2) * (1/2) = 1/4.
Why the other options are wrong
- A. This is the probability of spinning an odd number OR flipping a tails, but not both AND.
- B. Incorrect, perhaps a miscalculation.
- D. Incorrect, perhaps adding probabilities instead of multiplying.
Probability of Independent Events
For two independent events A and B, the probability that both A and B occur is the product of their individual probabilities: P(A and B) = P(A) * P(B).
- Events are independent if the outcome of one does not influence the other.
- Common examples include coin flips, dice rolls, or drawing with replacement.
- The keyword 'AND' often suggests multiplying probabilities for independent events.
Memory trick: Separate chances, multiply for both.