Question
3. Question 3. If a coin is flipped twice, the probability that it lands heads up both times is: a) \( 1 / 4 \) b) \( 1 / 2 \) c) \( 3 / 4 \) d) 1
Ask by Lee Rodriguez. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The probability of getting heads both times is \( \frac{1}{4} \).
Solution
To determine the probability that a coin lands heads up both times when flipped twice, we'll analyze the possible outcomes.
**Total Possible Outcomes:**
When a fair coin is flipped twice, each flip has two possible outcomes: Heads (H) or Tails (T). Therefore, the total number of possible outcomes is:
- First flip: H or T
- Second flip: H or T
This results in the following four equally likely outcomes:
1. HH
2. HT
3. TH
4. TT
**Favorable Outcome:**
We're interested in the specific outcome where both flips result in heads (HH). There is only **1** favorable outcome out of the four possible.
**Calculating Probability:**
Probability \( P \) is calculated as:
\[
P(\text{Both heads}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{4}
\]
**Answer:**
a) \( \frac{1}{4} \)
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
When you flip a coin, there are two possible outcomes: heads (H) or tails (T). Every flip operates independently, so the probability of getting heads on one flip is \( 1/2 \). If you flip the coin twice, the probability of getting heads both times is calculated by multiplying the probabilities of each individual flip: \( 1/2 \times 1/2 = 1/4 \). So, the answer is a) \( 1 / 4 \)! In a more playful sense, think of it this way: if you have a magic coin that likes to play tricks, by the time you've flipped it twice, it's like asking it to pull off two headstands in a row—pretty rare! So, enjoy that 1 out of 4 odds; it might be a while before your coin impresses you again!
