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Chapter 5: Problem 55

Imagine flipping three fair coins. a. What is the theoretical probability that all three come up heads? b. What is the theoretical probability that the first toss is tails AND the next two are heads?

Short Answer

Expert verified
a. The theoretical probability that all three coins come up heads is 0.125 or 12.5%. b. The theoretical probability that the first toss is tails and the next two are heads is also 0.125 or 12.5%

Step by step solution

01

Title

Firstly, calculate total outcomes. There are two possible results (heads or tails) for each coin flip. Therefore, with three coins, the total number of outcomes can be calculated as \(2^3 = 8\). This is because each toss is an independent event and doesn't influence the results of the others.
02

Title

Next, find the probability of getting three heads. The favorable outcome here is just one - that is all coins showing heads. So, probability is favorable outcomes divided by total outcomes. Here, it equals \(1/8 = 0.125\). This means that there's a 0.125 or 12.5% chance getting all heads when flipping three coins.
03

Title

Finally, uncover the probability of the sequence tails, heads and heads. Since the occurrence of heads or tails in each toss is independent, the compound probability can be found by multiplying the probabilities of each individual event. Hence, this calculates to \(0.5 * 0.5 * 0.5 = 0.125\) or 12.5%, indicating the probability obtaining a tail, followed by two heads.

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