Question

At a hot air balloon festival, Brendan made note of how many passengers were in each balloon and the color of each balloon. Blue Yellow Green Orange Purple 7 1 passenger 10 7 2 8 8 1 2 passengers 3 1 4 Are the events "the hot air balloon contains 1 passenger" and "the hot air balloon is orange" independent? yes no

Answer 1

In order to have independents events, we need to verify the following equation:

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

If event A is "the hot air balloon contains 1 passenger", the probability of this event is the sum of the number of balloons with 1 passenger divided by the total number of balloons:

$\begin{gathered} P(A)=\frac{7+10+7+2+8}{7+10+7+2+8+8+1+3+1+4} \\ P(A)=\frac{34}{51}=\frac{2}{3} \end{gathered}$

If event B is "the hot air balloon is orange