Bot GPT 4-o mini To find the probability that the number of cube rolls was 6 given that the coin landed on heads, we can use conditional probability.
We need to calculate the following:
P(Cube Rolls = 6 | Heads) = P(Heads | Cube Rolls = 6) * P(Cube Rolls = 6) / P(Heads)
From the table:
- Total Heads = 59
- Heads when Cube Rolls = 6 = 6
- Total Rolls (which is counts of all cube rolls, as given) = 100
We can find:
- P(Heads) = Total Heads / Total Rolls = 59 / 100
- P(Cube Rolls = 6) = (Total for 6) / Total Rolls = 16 / 100
Now, we also find:
- P(Heads | Cube Rolls = 6) = Heads when Cube Rolls = 6 / Total for cube rolls = 6 / 16
Now we can use the formula for conditional probability:
Using Bayes' theorem:
P(Cube Rolls = 6 | Heads) = (P(Heads | Cube Rolls = 6) * P(Cube Rolls = 6)) / P(Heads)
Filling in the values:
P(Heads | Cube Rolls = 6) = 6/16
P(Cube Rolls = 6) = 16/100
P(Heads) = 59/100
Now:
P(Cube Rolls = 6 | Heads) = (6/16) * (16/100) / (59/100)
Simplifying gives:
= (6/16) / (59/100)
= (6 / 16) * (100 / 59)
= (600 / 944)
= 75 / 118
However, there’s a simpler way to calculate the result directly because we just want:
P(Cube Rolls = 6 | Heads) = Heads when Cube Rolls = 6 / Total Heads
= 6 / 59
Putting it all together, we find:
The probability that the number of cube rolls was 6 given that the coin landed on heads is:
6 / 59
Among the choices given:
- 6100
- Start Fraction 6 over 100 End Fraction
- 659
- Start Fraction 6 over 59 End Fraction (This is correct)
- Start Fraction 6 over 16 End Fraction
- 596
The correct response is Start Fraction 6 over 59 End Fraction.
1 answer