Math Problem Statement
Three coins are tossed. Success is defined as getting a head. What is the probability that the toss will result in 0 head? Round the result to 3 places after decimal.
Solution
To find the probability of getting 0 heads when three coins are tossed, we can use the concept of binomial probability.
In this scenario:
- Each coin has 2 possible outcomes: head (H) or tail (T).
- There are a total of possible outcomes when three coins are tossed.
- We define success as getting a head.
We need to calculate the probability of getting exactly 0 heads (i.e., all tails).
First, let's enumerate the outcomes:
- HHH
- HHT
- HTH
- HTT
- THH
- THT
- TTH
- TTT
Only one of these outcomes results in 0 heads: TTT.
Now, calculate the probability:
Convert this fraction to a decimal and round to three decimal places:
Thus, the probability of getting 0 heads when three coins are tossed is:
Would you like further details or have any questions? Here are some related questions for deeper understanding:
- What is the probability of getting exactly 1 head in three coin tosses?
- What is the probability of getting exactly 2 heads in three coin tosses?
- What is the probability of getting exactly 3 heads in three coin tosses?
- How would the probability change if we tossed 4 coins instead of 3?
- What is the probability of getting at least 1 head in three coin tosses?
- How many possible outcomes result in getting at least 2 heads in three coin tosses?
- What is the expected number of heads in three coin tosses?
- How would you calculate the probability of getting exactly 0 heads using the binomial formula?
Tip: When dealing with probabilities of multiple events, visualizing all possible outcomes using a tree diagram or a probability table can greatly aid in understanding and solving the problem.
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Math Problem Analysis
Mathematical Concepts
Probability
Binomial distribution
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9