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Of 1000 students surveyed, 490 were boys and 320 had bicycles. of those who had bicycles, 130 were girls. what is the probability that a student surveyed was either a boy or had a bicycle?

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CintiaSalazar

By definition of probability, the probability that a student surveyed was either a boy or had a bicycle is 62%.

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.

Events and probability in this case

In first place, let's define the following events:

  • A: The event that a student surveyed was a boy.
  • B: The event that  a student surveyed had a bicycle.

Then you know:

  • P(A)= [tex]\frac{490}{1000}[/tex]=0.49= 49%
  • P(B)= [tex]\frac{320}{1000}[/tex]= 0.32= 32%
  • P(A and B)= P(A∩B)= [tex]\frac{190}{1000}[/tex]= 0.19= 19% [320 students had bicycles. Of those who had bicycles, 130 were girls. Then, 190 were boys.]

In this case, considering the definition of union of eventes, the probability that a student surveyed was either a boy or had a bicycle is calculated as:

P(A∪B)= P(A) + P(B) -P(A∩B)

P(A∪B)= 0.49 + 0.32 -0.19

P(A∪B)= 0.62= 62%

Then, the probability that a student surveyed was either a boy or had a bicycle is 62%.

Learn more about probability:

brainly.com/question/25839839

brainly.com/question/26038361

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