Question

Who eats breakfast? Refer to Exercise 68. Are events B and M independent? Justify your answer.

Short answer

Yes, not independent.

Step-by-step solution

Step 1. Given Information

The two-way table depicts the $595$ pupils that responded to a breakfast survey at school. Consider the following scenario: $B$eats breakfast every day, and $M$ is a man.

Step 2. Concept Used

The number of favorable outcomes divided by the total number of possible outcomes equals probability. As a result, the following is a definition of conditional probability:

Step 3. Calculation

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

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

If the occurrences $B$and $M$ are independent, they should be identical. As a result, they are not self-sufficient.