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

If event B is "the hot air balloon is orange