By definition of probability, the probability that a person surveyed was either male or had a cell phone is [tex]\frac{450}{600}[/tex]= 0.75
Definition of Probabitity
Probability is the greater or lesser possibility that a certain event will occur.
In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.
Union of events
The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".
The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:
P(A∪B)= P(A) + P(B) -P(A∩B)
The intersection of events, A ∩ B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.
Probability that a person surveyed was either male or had a cell phone
In first place, let's define the following events:
- M: the person surveyed was male.
- C: the person surveyed had a cell phone.
The probability that a person surveyed was either male or had a cell phone is calculated as:
P(M∪C)= P(M) + P(C) -P(M∩C)
In this case, you know:
- P(M)= [tex]\frac{220}{600}[/tex]
- P(C)= [tex]\frac{350}{600}[/tex]
- P(M∩C)= [tex]\frac{120}{600}[/tex] (Of the 350 people who have cell phones, 230 are female. This means the remaining 120 people with cell phones are male.)
Replacing in the definition of probability:
P(M∪C)= [tex]\frac{220}{600}[/tex] + [tex]\frac{350}{600}[/tex] - [tex]\frac{120}{600}[/tex]
Solving:
P(M∪C)= [tex]\frac{220+350 -120}{600}[/tex]
P(M∪C)= [tex]\frac{450}{600}[/tex]= 0.75
Finally, the probability that a person surveyed was either male or had a cell phone is [tex]\frac{450}{600}[/tex]= 0.75
Learn more about probability:
brainly.com/question/25839839
brainly.com/question/26038361
