Question

Use the image to answer the question.

A Venn diagram shows two intersecting circles. Circle 1 represents event A, 3 and 5. Circle 2 represents event B, 6, 8, 10, and 12. The intersection of both the circles is labeled 7, 9, and 11. The space outside the circles is labeled 2 and 4.

The Venn diagram represents the results of the experiment of rolling two fair, six-sided number cubes and adding the sum of the two rolls. Consider event A
as “sum is odd” and event B
as “sum is 6 or greater.” Find the probability that the sum is odd, given that the sum is 6 or greater.

(1 point)
Responses

37

Start Fraction 3 over 7 End Fraction

312

Start Fraction 3 over 12 End Fraction

35

Start Fraction 3 over 5 End Fraction

512

Answer 1

We want P(sum is odd | sum ≥ 6) = P(A ∩ B) / P(B).

Given the Venn diagram, B = {6,7,8,9,10,11,12} (7 sums) and A ∩ B = {7,9,11} (3 sums). Treating each sum equally, the conditional probability is 3/7.