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Chapter 2: Problem 109

A coin is tossed 3 times, and 2 heads and 1 tail fall. What is the probability that the first toss was heads?

Short Answer

Expert verified
The probability of the first toss being heads is \(\frac{2}{3}\) or approximately 0.67.

Step by step solution

01

Determine possible outcomes

If there are 2 heads and 1 tail in total, there are 3 possible outcomes we can get: 1. Heads - Heads - Tails (HHT) 2. Heads - Tails - Heads (HTH) 3. Tails - Heads - Heads (THH)
02

Identify the event of interest

For our problem, we are interested in the event in which the first toss results in heads. Out of the three outcomes identified in Step 1, there are 2 in which the first toss is heads: 1. Heads - Heads - Tails (HHT) 2. Heads - Tails - Heads (HTH)
03

Calculate the probability

Now, let's calculate the probability of the first toss being heads. There are a total of 3 possible outcomes and 2 outcomes that satisfy our event of interest. Therefore, the probability of the first toss being heads is given by: Probability (First toss is heads) = \(\frac{\text{Number of outcomes with first toss Heads}}{\text{Total number of possible outcomes}}\) Substitute the values we found in Step 1 and Step 2: Probability (First toss is heads) = \(\frac{2}{3}\) So, the probability of the first toss being heads is \(\frac{2}{3}\), or approximately 0.67.

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