Chapter 5.3, Problem 70E

To determine

To check: whether the events “D” and “F” are independent.

Answer to Problem 70E

Yes, not independent.

Explanation of Solution

Given:

The two-way table describes the 595 students who responds to a school survey about breakfast.

Consider event B eats regularly breakfast, M is male.

	Male	Female	Total
Eats break-fast regularly	190	110	300
Doesn’t eats break-fast regularly	130	165	195
Total	320	275	595

Calculation:

From part (a) and part (b) in exercise 68,

  $P\left(B|M\right)=\frac{190}{320}\approx 0.5938$

  $P\left(B\right)=\frac{300}{595}\approx 0.5042$ .

There probability should be identical if the events B and M are independent.

Thus, they are not independent.