Question

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 lunch. Are the two events “kids eating pizza” and ”kids eating tacos” independent events?

Answer 1

Answer:

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

Step-by-step 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

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

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