Question

use the theoretical method to determine the probability of the following outcome and event. state any assumptions made.

tossing two coins and getting either one head or two heads

choose the correct answer below.

a. assuming that each coin is fair and is equally likely to land heads or tails, the probability is \\(\frac{4}{3}\\)
b. assuming that each coin is fair and is equally likely to land heads or tails, the probability is \\(2 \times 2\\)
c. assuming that each coin is fair and is equally likely to land heads or tails, the probability is \\(\frac{1}{2}\\)
d. assuming that each coin is fair and is equally likely to land heads or tails, the probability is \\(\frac{3}{4}\\)

Explanation:

Identify the sample space

Using the Equally Likely Outcomes and Fair Coin Probability knowledge points

$$ S = \{HH, HT, TH, TT\} $$

$$ n(S) = 4 $$

Identify the favorable outcomes

Using the Theoretical Probability knowledge point

$$ E = \{HT, TH, HH\} $$

$$ n(E) = 3 $$

Calculate the probability

Using the Theoretical Probability knowledge point

$$ P(E) = \frac{n(E)}{n(S)} = \frac{3}{4} $$

Match with the correct option

Using the Theoretical Probability knowledge point
The correct option is D, which assumes fair coins and states the probability is \(\frac{3}{4}\).

Answer:

• A. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \(\frac{4}{3}\)
• B. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \(2 \times 2\)
• C. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \(\frac{1}{2}\)
• D. Assuming that each coin is fair and is equally likely to land heads or tails, the probability is \(\frac{3}{4}\) (Correct answer)