Use the table to answer the question.

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

616
Start Fraction 6 over 16 End Fraction

659
Start Fraction 6 over 59 End Fraction

596
Start Fraction 59 over 6 End Fraction

6100
Start Fraction 6 over 100 End Fraction

Answer 1

To find the probability that the number of cube rolls was 6 given that the coin flip landed on heads, we can use the formula for conditional probability:

\[ P(A|B) = \frac{P(A \cap B)}{P(B)} \]

Where:

• \(A\) is the event that the cube was rolled 6 times.
• \(B\) is the event that the coin landed on heads.

From the table:

• The total number of times the coin flipped to heads (event \(B\)) is 59.
• The number of times the cube was rolled 6 times and the coin landed on heads (event \(A \cap B\)) is 6.

Now, we can substitute these values into our formula:

\[ P(\text{Cube Rolls} = 6 | \text{Heads}) = \frac{\text{Number of Heads and Cube Rolls = 6}}{\text{Total Number of Heads}} = \frac{6}{59} \]

Thus, the correct response is:

\(\frac{6}{59}\)

So the answer is: 659