Question

Question Use the table to answer the question. Number of Cube Rolls Coin Flips Cube Rolls=1 Cube Rolls=2 Cube Rolls=3 Cube Rolls=4 Cube Rolls=5 Cube Rolls=6 Total Heads 9 15 12 8 9 6 59 Tails 8 6 11 12 14 10 61 Total 17 21 23 20 23 16 100 Given that a coin is flipped and lands on heads, what is the probability that the number cube was rolled 6 times? (1 point) Responses 6100 Start Fraction 6 over 100 End Fraction 659 Start Fraction 6 over 59 End Fraction 616 Start Fraction 6 over 16 End Fraction 596

Answer 1

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:

1. **Total Heads** = 59
2. **Heads when Cube Rolls = 6** = 6
3. **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**.