Problem

3. A quarter is tossed into the air and lands. Then, a nickel is tossed into the air. a) List all the possible outcomes. b) What is the probability of landing one head and one tail? c) What is the probability of a head followed by a tail? d) Fxnlain the difference between $P(H, T)$ and $P(H$ then $T)$.

Solution

Step 1 :a) The possible outcomes are: \( (H, H), (H, T), (T, H), (T, T) \)

Step 2 :b) The probability of landing one head and one tail is \( \boxed{0.5} \)

Step 3 :c) The probability of a head followed by a tail is \( \boxed{0.25} \)

Step 4 :d) The difference between \( P(H, T) \) and \( P(H \text{ then } T) \) is that \( P(H, T) \) represents the probability of getting one head and one tail in any order, while \( P(H \text{ then } T) \) represents the probability of getting a head specifically on the first toss (quarter) and a tail specifically on the second toss (nickel). In this case, \( P(H, T) = 0.5 \) and \( P(H \text{ then } T) = 0.25 \).

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Source: https://solvelyapp.com/problems/21344/

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