Question
Eva flips three fair coins and notes the result. She repeats this experiment 10 times. In Eva's trials, all three coins land on tails 2 of the ten times and all three coins land on heads 1 of the ten times.
Which of these statements are true? Choose the two correct answers.
A. There are 6 possible outcomes for the experiment of flipping 3 coins.
B. The theoretical probability that all three coins will land on heads is 1/8
C. Eva found the experimental probability that all three coins land on tails to be 1/5.
D. The theoretical probability that at least one of the three coins lands on tails is 3/8 .
E. Eva's experiment is flawed because the theoretical probability of heads on all three
coins are different from the experimental probability.
Which of these statements are true? Choose the two correct answers.
A. There are 6 possible outcomes for the experiment of flipping 3 coins.
B. The theoretical probability that all three coins will land on heads is 1/8
C. Eva found the experimental probability that all three coins land on tails to be 1/5.
D. The theoretical probability that at least one of the three coins lands on tails is 3/8 .
E. Eva's experiment is flawed because the theoretical probability of heads on all three
coins are different from the experimental probability.
Answers
Answered by
GPT-4o mini
To evaluate the statements, let's break down the probabilities and the outcomes of flipping three fair coins:
1. **Outcome of Flipping 3 Coins**: Each coin has 2 possible outcomes (Heads or Tails), and for 3 coins, the total number of outcomes is:
\[ 2^3 = 8 \]
So, the possible outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Thus, Statement A, "There are 6 possible outcomes for the experiment of flipping 3 coins," is **false**.
2. **Theoretical Probability of All Heads**:
The probability of getting all heads (HHH) is:
\[ P(\text{HHH}) = \frac{1}{8} \]
Thus, Statement B, "The theoretical probability that all three coins will land on heads is 1/8," is **true**.
3. **Experimental Probability of All Tails**:
Eva has 2 trials out of 10 where all three coins landed on tails (TTT). The experimental probability is:
\[ P(\text{TTT}) = \frac{2}{10} = \frac{1}{5} \]
Thus, Statement C, "Eva found the experimental probability that all three coins land on tails to be 1/5," is **true**.
4. **Theoretical Probability of At Least One Tail**:
To find the theoretical probability of getting at least one tail, we'll first find the probability of getting no tails (all heads, HHH):
\[ P(\text{at least one T}) = 1 - P(\text{HHH}) = 1 - \frac{1}{8} = \frac{7}{8} \]
Statement D, "The theoretical probability that at least one of the three coins lands on tails is 3/8," is **false**.
5. **Flaw in the Experiment**:
The statement argues that Eva's experiment is flawed because the theoretical probability is different from the experimental probability. However, there is nothing inherently flawed about having different theoretical and experimental probabilities. This is a common occurrence in probability and statistics due to sample size and randomness. Thus, Statement E, "Eva's experiment is flawed because the theoretical probability of heads on all three coins is different from the experimental probability," is **false**.
In summary, the correct answers are:
- **B**: The theoretical probability that all three coins will land on heads is 1/8.
- **C**: Eva found the experimental probability that all three coins land on tails to be 1/5.
1. **Outcome of Flipping 3 Coins**: Each coin has 2 possible outcomes (Heads or Tails), and for 3 coins, the total number of outcomes is:
\[ 2^3 = 8 \]
So, the possible outcomes are: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.
Thus, Statement A, "There are 6 possible outcomes for the experiment of flipping 3 coins," is **false**.
2. **Theoretical Probability of All Heads**:
The probability of getting all heads (HHH) is:
\[ P(\text{HHH}) = \frac{1}{8} \]
Thus, Statement B, "The theoretical probability that all three coins will land on heads is 1/8," is **true**.
3. **Experimental Probability of All Tails**:
Eva has 2 trials out of 10 where all three coins landed on tails (TTT). The experimental probability is:
\[ P(\text{TTT}) = \frac{2}{10} = \frac{1}{5} \]
Thus, Statement C, "Eva found the experimental probability that all three coins land on tails to be 1/5," is **true**.
4. **Theoretical Probability of At Least One Tail**:
To find the theoretical probability of getting at least one tail, we'll first find the probability of getting no tails (all heads, HHH):
\[ P(\text{at least one T}) = 1 - P(\text{HHH}) = 1 - \frac{1}{8} = \frac{7}{8} \]
Statement D, "The theoretical probability that at least one of the three coins lands on tails is 3/8," is **false**.
5. **Flaw in the Experiment**:
The statement argues that Eva's experiment is flawed because the theoretical probability is different from the experimental probability. However, there is nothing inherently flawed about having different theoretical and experimental probabilities. This is a common occurrence in probability and statistics due to sample size and randomness. Thus, Statement E, "Eva's experiment is flawed because the theoretical probability of heads on all three coins is different from the experimental probability," is **false**.
In summary, the correct answers are:
- **B**: The theoretical probability that all three coins will land on heads is 1/8.
- **C**: Eva found the experimental probability that all three coins land on tails to be 1/5.