To find the relative frequency for the event "tails" for each friend, we can use the formula:
\[ \text{Relative Frequency} = \frac{\text{Number of Tails}}{\text{Total Flips}} \]
Each friend flipped a coin 87 times, so the total number of flips for each friend is 87. We will calculate the relative frequency of tails for each friend.
Friend 1:
- Tails: 59
- Total Flips: 87
\[ \text{Relative Frequency for Friend 1} = \frac{59}{87} \approx 0.6764 \]
Rounding to the nearest hundredth:
0.68
Friend 2:
- Tails: 47
- Total Flips: 87
\[ \text{Relative Frequency for Friend 2} = \frac{47}{87} \approx 0.5402 \]
Rounding to the nearest hundredth:
0.54
Friend 3:
- Tails: 50
- Total Flips: 87
\[ \text{Relative Frequency for Friend 3} = \frac{50}{87} \approx 0.5747 \]
Rounding to the nearest hundredth:
0.57
Now, to combine the results of all three friends, we sum the number of heads and tails:
- Total Heads: 28 (Friend 1) + 40 (Friend 2) + 37 (Friend 3) = 105
- Total Tails: 59 (Friend 1) + 47 (Friend 2) + 50 (Friend 3) = 156
Combined total flips is: \[ \text{Total Flips} = 105 + 156 = 261 \]
Relative frequency for the event "tails" when all three friends combine their results:
\[ \text{Relative Frequency for Combined Results} = \frac{156}{261} \approx 0.5977 \]
Rounding to the nearest hundredth:
0.60
Final Expected Value After 870 Flips
If each friend flips a coin 870 times, we can reason that the relative frequency will tend toward the actual probability of tails in a fair coin toss, which is 0.5.
Thus, after flipping a larger number of coins (870 each), we would expect the relative frequency for the event "tails" to be close to 0.50.