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Chapter 23: Problem 534

A penny is to be tossed 3 times. What is the probability there will be 2 heads and 1 tail?

Short Answer

Expert verified
The probability of getting 2 heads and 1 tail when tossing a penny 3 times is \(\frac{3}{8}\) or approximately 0.375.

Step by step solution

01

Determine the Total Number of Possible Outcomes

Since we are tossing a penny 3 times, there are two possible outcomes for each toss (heads or tails). To find the total number of possible outcomes, we multiply the number of possible outcomes at each stage: Total possible outcomes = \(2^3\) = 8 (2 choices for the first toss, 2 choices for the second toss, and 2 choices for the third toss.)
02

Determine the Number of Favorable Outcomes (2 heads, 1 tail)

Next, we'll find the number of ways the desired outcome can occur. We can have 2 heads and 1 tail in the following possible sequences: 1. HHT 2. HTH 3. THH There are 3 favorable outcomes.
03

Calculate the Probability

Now, we'll calculate the probability of getting the desired outcome by dividing the number of favorable outcomes by the total possible outcomes: Probability of 2 heads and 1 tail = \(\frac{Favorable\: Outcomes}{Total\: Possible\: Outcomes}\) Probability = \(\frac{3}{8}\) So, the probability of getting 2 heads and 1 tail when tossing a penny 3 times is \(\frac{3}{8}\) or approximately 0.375.

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