Question

two fair coins are tossed (say a dime and a quarter). the two possible outcomes for a single coin are heads, h, and tails, t. give each of the following.
(a) the sample space
(b) the probability of heads on the dime
(c) the probability of heads on the quarter
(d) the probability of getting both heads
(e) the probability of getting the same outcome on both coins

(a) the sample space is
(use a comma to separate answers as needed.)

Explanation:

Step1: Determine sample space

Each coin has 2 outcomes. For two coins (dime and quarter), using the rule of counting, the sample space \(S=\{(h,h),(h,t),(t,h),(t,t)\}\).

Step2: Calculate probability of heads on dime

Number of outcomes with dime as heads: 2 \((h,h),(h,t)\). Total outcomes \(n = 4\). Probability \(P=\frac{2}{4}=\frac{1}{2}\).

Step3: Calculate probability of heads on quarter

Number of outcomes with quarter as heads: 2 \((h,h),(t,h)\). Total outcomes \(n = 4\). Probability \(P=\frac{2}{4}=\frac{1}{2}\).

Step4: Calculate probability of both heads

Number of outcomes with both heads: 1 \((h,h)\). Total outcomes \(n = 4\). Probability \(P=\frac{1}{4}\).

Step5: Calculate probability of same outcome

Number of outcomes with same outcome: 2 \((h,h),(t,t)\). Total outcomes \(n = 4\). Probability \(P=\frac{2}{4}=\frac{1}{2}\).

Answer:

(a) \((h,h),(h,t),(t,h),(t,t)\)
(b) \(\frac{1}{2}\)
(c) \(\frac{1}{2}\)
(d) \(\frac{1}{4}\)
(e) \(\frac{1}{2}\)