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The principal of a high school needs to plan seating for commencement. The following two-way table displays data for the students who are involved in this year's commencement ceremony.
Grade level In choir Not in choir TOTAL
Junior 15 3 18
Senior 23 436 459
Other 3 0 3
TOTAL 41 439 480
For these students, are the events "senior" and "not in choir" mutually exclusive?
Find the probability that a randomly selected student from this group is a senior OR is not in choir.

Respuesta :

Answer: 77/80= 0.9625

Step-by-step explanation:

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Using the principle of probability, it can be concluded that :

  • Events Senior and Not in Choir are not mutually exclusive
  • P(Senior OR Not in choir) = 0.9625

To test if the events "senior" and "not in choir" are mutually exclusive :

  • P(Senior n Not in choir) = 0
  • P(S) = probability of Senior
  • P(N) = probability of Not in choir

From the table :

  • P(Senior n Not in choir) = 436/480

Hence, the events are not mutually exclusive.

Probability that a randomly selected student is a Senior Or is not in choir :

  • P(SuN) = P(S) + P(N) - P(SnN)

P(SuN) = (459/480) + (439/480) - (436/480)

P(SuN) = 0.9625

Therefore, the probability that a randomly selected student is a 'Senior' or 'Not in Choir' is 0.9625.

Learn more :https://brainly.com/question/18405415

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