Make a Venn diagram to visualize the situation. Then decide if the events are disjoint or not.
9/20, or 0.45
Practice makes perfect
We are throwing a dart. It is equally likely that the dart will hit any point inside the board. We pop the balloon. We want to find the probability that the balloon is red or blue. We will mark an event of popping a red balloon as A, and the event of popping a blue balloon as B. Let's make a Venn diagram considering these two events.
There are no balloons that can be red and blue at the same time, so events R and B are disjoint. We are interested in the probability of A or B, which is a compound event. Recall how we calculate the probability of compound events when the events are disjoint.
P(AorB)=P(A)+P(B)
We need to find the probabilities of events A and B. To do so we will divide the number of favorable outcomes by the total number of outcomes. We know that we popped a balloon, so the number of possible outcomes is the number of balloons on the board, 20. Note that the number of red balloons is 6, and the number of blue balloons is 3.
Event
Number of Favorable Outcomes
Total Number of Outcomes
Probability
A
6
20
6/20
B
3
20
3/20
Knowing the probabilities of events A and B, we can substitute them into the formula for the probability of disjoint compound events and simplify.
