Question

At a hot air balloon festival, Shane made note of how many passengers were in each balloon and the color of each balloon. 1 passenger 2 passengers Blue 10 6 Yellow 9 6 What is the probability that a randomly selected hot air balloon is yellow or contains 1 passenger? Simplify any fractions.

Answer 1

The searche probability is

$P(\text{yellow}\cup1passenger)$

which is equal to

$P(\text{yellow}\cup1passenger)=P(\text{yellow})+P(1passenger)-P(\text{yellow}\cap1passenger)$

From our table, P(yellow)=9+6=15, P(ipassenger)=10+9=19 and P(yellow n 1passenger)=9, then

we have

$P(\text{yellow}\cup1passenger)=\frac{15}{31}+\frac{19}{31}-\frac{9}{31}$

where 31 is the sum of all values (grand total). Then, the answer is

$P(\text{yellow }\cup1passenger)=\frac{25}{31}$