Probability of Events That Are Not Mutually Exclusive
If two events A and B are not mutually exclusive, then the probability that A or B occurs can be calculated using the following formula.
P(AorB)=P(A)+ P(B)-P(AandB)
We can use this formula.
P(Even or less than5)= P(Even)+P(Less than5) -P(Even and less than5)
There are 402= 20 even numbers in the range 1-40. Also, there is a total of 40 tickets in the bag. Using this information we can calculate P(Even), which is the probability that a randomly chosen ticket is even.
P(Even)=20/40=0.5
The tickets that are less than 5 are 1, 2, 3, and 4 — a total of 4 tickets. Let's use this information to calculate P(Less than5), which is the probability that a randomly selected ticket is less than 5.
P(Less than5)=4/40=0.1
Now, we will calculate P(Even and less than5). There are only 2 tickets that are both even and less than 5. These are the tickets 2 and 4.
P(Even and less than5)=2/40=0.05
Finally, we are ready to calculate the probability P(Even or less than5).
P(Even or less than5)= 0.5+0.1-0.05=0.55
The probability that a randomly chosen ticket has a number that is even or less than 5 is 0.55.
b In this part we will calculate the probability that a randomly chosen ticket is greater than 30 or less than 10.
P(Greater than30or less than10)=?
Since a number cannot be greater than 30 and less than 10 at the same time, the events are mutually exclusive. Let's recall the formula for the probability of mutually exclusive events.
Probability of Events That Are Mutually Exclusive
If two events A and B are mutually exclusive, then the probability that A or B occurs can be calculated using the following formula.
P(AorB)=P(A)+ P(B)
We can use this formula.
P(Greater than30or less than10)=
P(Greater than30)+P(less than10)
There are 10 tickets that are greater than 30.
Greater than 30:
31,32,33,34,35,36,37,38,39,40
In total, there are 40 tickets in the bag. Using this information we can calculate P(Greater than30), which is the probability that a randomly selected ticket is greater than 30.
P(Greater than30)=10/40=0.25
Now, let's calculate the probability that a randomly chosen ticket is less than 10. There are 9 tickets that are less than 10.
Less than 10: 1,2,3,4,5,6,7,8,9
We can calculate the probability P(Less than10) using this information.
P(Less than10)=9/40=0.225
Finally, we are ready to calculate the probability that a randomly chosen ticket is greater than 30 or less than 10.
P(Greater than30or less than10)= 0.25+0.225=0.475
We found that the probability is equal to 0.475.
