bebuca02p353ch bebuca02p353ch
  • 07-04-2024
  • Mathematics
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Given P(A) = 0.25, P(B) = 0.38, and P(A or B) = 0.63, are events A and B mutually exclusive?

Respuesta :

jimthompson5910 jimthompson5910
  • 07-04-2024

Answer:  Yes

Work Shown

P(A and B) = P(A) + P(B) - P(A or B)

P(A and B) = 0.25 + 0.38 - 0.63

P(A and B) = 0

The result of zero means events A and B cannot happen at the same time, which directly leads to the events being mutually exclusive aka disjoint.

Side note: If A and B are disjoint, then P(A or B) = P(A)+P(B). We see this is the case since P(A)+P(B) = 0.25+0.38 = 0.63 = P(A or B).

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