Question

Green River State Park has two popular hiking trails: Overlook Trail and High Ridge Trail. On one particular day, 80 hiking groups used the trails: 40 groups used Overlook Trail and 40 groups used High Ridge Trail. Of the 40 groups that used Overlook Trail, 30 groups had children and 10 groups had no children. Of the 40 groups that used High Ridge Trail, 15 groups had children and 25 groups had no children. Consider the following events.

H: A hiking group uses High Ridge Trail.
C: A hiking group has children.
Which statement is true about events H and C?

A. Events H and C are independent and P(H|C) < P(C|H).

B. Events H and C are dependent and P(H|C) < P(C|H).

C. Events H and C are independent and P(H|C) = P(C|H).

D. Events H and C are dependent and P(H|C) = P(C|H).

Answer 1

B. Events H and C are dependent and P(H|C) < P(C|H)

Explanation:

The ratios of groups with children to hiking groups on the trail are different for the two trails.

P(H|C) = 15/45 = 1/3

P(C|H) = 15/40 = 3/8

1/3 < 3/8 so the comparison of choice B is appropriate.