Start with identifying if the events of us and the friend winning are disjoint or not. Then use the formula for the probability of compound events.
70 %, or 0.7
Practice makes perfect
We and a friend are among several candidates for class president. We estimated that there is a 45 % chance that we will win, and a 25 % chance that our friend will win. We want to find the probability that either we or our friend will win the election. To do so we will need the formula for the probability of compound events. First let's think if our events are disjoint or not.
Disjoint Events
The events are disjoint, or mutually exclusive, when they have no outcomes in common.
If we win, there is no possibility that our friend will win. If they win, there is no possibility that we will win. Therefore, the events of us winning and our friend winning are disjoint. Recall the formula for the probability of compound events if the events are disjoint.
P(AorB)=P(A)+P(B)
In our case event A is the event of us winning the election, and event B is the event of our friend winning. The probability that we will win is 45 %, and the probability that our friend will win is 25 %. Let's substitute these values into the formula and simplify.
