What is the probability of getting 2 heads up and 1 tail up when flipping three coins?
A. $\frac{1}{6}$
B. $\frac{1}{4}$
C. $\frac{3}{8}$
D. $\frac{2}{3}$
Answer (2)
The probability of getting exactly 2 heads and 1 tail when flipping three coins is 8 3 . This is calculated by identifying the favorable outcomes and dividing them by the total possible outcomes. The total outcomes are 8, and the favorable outcomes for 2 heads and 1 tail are 3.
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List all possible outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH, TTT.
Identify outcomes with 2 heads and 1 tail: HHT, HTH, THH.
Calculate the probability: 8 3 .
The probability of getting 2 heads and 1 tail is 8 3 .
Explanation
Understand the problem Let's analyze the problem. We want to find the probability of getting exactly 2 heads and 1 tail when flipping three coins. Each coin flip is an independent event, and there are two possible outcomes for each flip: heads (H) or tails (T).
List all possible outcomes First, let's list all the possible outcomes when flipping three coins. Each outcome is a sequence of three letters, where each letter is either H or T. The possible outcomes are:
HHH, HHT, HTH, THH, HTT, THT, TTH, TTT
There are a total of 8 possible outcomes.
Identify favorable outcomes Next, let's identify the outcomes that have exactly 2 heads and 1 tail. These are:
HHT, HTH, THH
There are 3 such outcomes.
Calculate the probability Now, we can calculate the probability of getting exactly 2 heads and 1 tail. The probability is the number of favorable outcomes divided by the total number of possible outcomes:
P ( 2 heads and 1 tail ) = Total number of possible outcomes Number of favorable outcomes = 8 3
So, the probability of getting 2 heads and 1 tail when flipping three coins is 8 3 .
Examples
Consider a game where you win if you get exactly 2 heads when flipping three coins. Knowing the probability, 8 3 , helps you understand your chances of winning and whether the game is fair. For instance, if the reward for winning is not high enough compared to the probability of winning, the game might not be worth playing.
