Math Problem Statement
The following table shows the frequency of outcomes when two distinguishable coins were tossed 4,800 times and the uppermost faces were observed. HINT [See Example 2.] Outcome HH HT TH TT Frequency 1,300 1,150 1,400 950 What is the relative frequency that heads comes up at least once? (Round your answer to four decimal places.)
Solution
To find the relative frequency that heads comes up at least once, let's first identify the relevant outcomes and frequencies.
The possible outcomes when two coins are tossed are:
- HH (both heads)
- HT (heads and tails)
- TH (tails and heads)
- TT (both tails)
We are interested in the outcomes where at least one head comes up. These outcomes are:
- HH (both heads)
- HT (heads and tails)
- TH (tails and heads)
Now, let's calculate the total frequency for these outcomes:
Next, the total number of trials is 4,800.
The relative frequency that heads comes up at least once is:
Now, let's compute that:
Thus, the relative frequency that heads comes up at least once is approximately 0.8021.
Would you like more details or have any questions? Here are 5 related questions to think about:
- What is the probability of getting two tails in this experiment?
- How would the relative frequency change if the total trials were different?
- What are the odds of getting exactly one head?
- Can you use this data to estimate the probability of heads or tails in a single coin toss?
- How would you calculate the relative frequency of tails showing up at least once?
Tip: When calculating relative frequencies, always ensure the total counts and event counts are accurate before dividing.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Probability
Relative Frequency
Formulas
Relative frequency = (Number of favorable outcomes) / (Total number of trials)
Theorems
Basic Probability Theorem
Suitable Grade Level
Grades 6-8
Related Recommendation
Probability of Getting at Least One Head in 1000 Coin Tosses
Calculate the Relative Frequency of Tails from 10 Coin Flips
Calculating Proportion of Heads After 100 Coin Tosses with Known Outcomes
Probability of Coin Tosses: One Head, First Head, and Alternating Heads and Tails
Understanding Coin Toss Probability and Expected Outcomes