On a field trip, there is a 55% chance of kids having pizza for lunch, a 20% chance of kids having tacos for lunch, and a 15% chance of kids having pizza and tacos together for …

Question

asked Aug 26, 2021 8.1k views

1 Answer

Jie · Answer 1 · 2021-09-02T04:10:36+0000

Answer:

$P(A \cap B) \\eq P(A)P(B)$ , which means that the two events “kids eating pizza” and ”kids eating tacos” are not independent events

Explanation:

Independent events:

Two events, A and B are independent, if:

$P(A \cap B) = P(A)P(B)$

In this problem:

Event A: Pizza for lunch

Event B: Tacos for luch

15% chance of kids having pizza and tacos together for lunch.

This means that
$P(A \cap B) = 0.15$

20% chance of kids having tacos for lunch

This means that
P(B) = 0.2

55% chance of kids having pizza for lunch

This means that
P(A) = 0.55

So

P(A)P(B) = 0.55*0.2 = 0.11

$P(A \cap B) \\eq P(A)P(B)$ , which means that the two events “kids eating pizza” and ”kids eating tacos” are not independent events