at a hot air balloon festival, kristen made note of how many passengers were in each balloon and the color…

at a hot air balloon festival, kristen made note of how many passengers were in each balloon and the color of each balloon.\nthe probability that a hot air balloon contains 10 or more passengers is 0.04, the probability that it is multicolored is 0.84, and the probability that it contains 10 or more passengers or is multicolored is 0.86.\nwhat is the probability that a randomly chosen hot air balloon contains 10 or more passengers and is multicolored?\nwrite your answer as a whole number, decimal, or simplified fraction.

at a hot air balloon festival, kristen made note of how many passengers were in each balloon and the color of each balloon.\nthe probability that a hot air balloon contains 10 or more passengers is 0.04, the probability that it is multicolored is 0.84, and the probability that it contains 10 or more passengers or is multicolored is 0.86.\nwhat is the probability that a randomly chosen hot air balloon contains 10 or more passengers and is multicolored?\nwrite your answer as a whole number, decimal, or simplified fraction.

Answer

Explanation:

Step1: Recall the formula

Use the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let $A$ be the event that a hot - air balloon contains 10 or more passengers and $B$ be the event that a hot - air balloon is multicolored.

Step2: Identify the given probabilities

We know that $P(A) = 0.04$, $P(B)=0.84$, and $P(A\cup B)=0.86$.

Step3: Solve for $P(A\cap B)$

Substitute the values into the formula: $0.86=0.04 + 0.84-P(A\cap B)$. Then, $P(A\cap B)=0.04 + 0.84-0.86$. $P(A\cap B)=0.02$

Answer:

$0.02$