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 23=82^3 = 8 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:

P(0 heads)=Number of favorable outcomesTotal number of possible outcomes=18P(\text{0 heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{8}

Convert this fraction to a decimal and round to three decimal places:

18=0.125\frac{1}{8} = 0.125

Thus, the probability of getting 0 heads when three coins are tossed is:

0.125\boxed{0.125}

Would you like further details or have any questions? Here are some related questions for deeper understanding:

  1. What is the probability of getting exactly 1 head in three coin tosses?
  2. What is the probability of getting exactly 2 heads in three coin tosses?
  3. What is the probability of getting exactly 3 heads in three coin tosses?
  4. How would the probability change if we tossed 4 coins instead of 3?
  5. What is the probability of getting at least 1 head in three coin tosses?
  6. How many possible outcomes result in getting at least 2 heads in three coin tosses?
  7. What is the expected number of heads in three coin tosses?
  8. 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