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

6100
Start Fraction 6 over 100 End Fraction

596
Start Fraction 59 over 6 End Fraction

659
Start Fraction 6 over 59 End Fraction

616
Start Fraction 6 over 16 End Fraction

Answer 1

To find the probability that the number of cube rolls is 6 given that the coin flip lands 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 there are 6 cube rolls.
• \( B \) is the event that the coin lands on heads.

From the table, we can see:

• The number of times the coin lands on heads (event \( B \)) is 59.
• The number of times the coin lands on heads and there are 6 cube rolls (event \( A \cap B \)) is 6.

Hence, we can calculate the conditional probability \( P(A|B) \):

\[ P(A|B) = \frac{\text{Number of heads and 6 cube rolls}}{\text{Total number of heads}} = \frac{6}{59} \]

So the probability that the number of cube rolls is 6 given that the coin shows heads is:

\[ \frac{6}{59} \]

Thus, the correct response is:

\[ \text{Start Fraction 6 over 59 End Fraction} \]