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Andrew [12]
2 years ago
11

Determine if the events A and B are independent. Show all steps.

Mathematics
1 answer:
zmey [24]2 years ago
4 0

<u><em></em></u>

Answer:

P(A U B )  = \frac{13}{25}

Step-by-step explanation:

<u><em>STEP:-1</em></u>

Given that events A and B are independent then

P(A ∩B ) = P(A) P(B)

Given that P(A) = 2/5 and P(B) = 1/5

<u><em>STEP:- 2</em></u>

P(A ∩B ) = P(A) P(B)

P(A U B) = P(A) +P(B) - P(A n B )

P(A U B ) = P(A) +P(B) - P(A) P(B)

<u><em>Step(iii):-</em></u>

<u><em></em></u>P(A U B ) = \frac{2}{5}  +\frac{1}{5} - \frac{2}{5} X \frac{1}{5}<u><em></em></u>

<u><em></em></u>P(A U B ) = \frac{3}{5}  - \frac{2}{5} X \frac{1}{5}<u><em></em></u>

<u><em></em></u>P(A U B ) = \frac{3}{5}  - \frac{2}{25}<u><em></em></u>

<u><em></em></u>P(A U B ) = \frac{15-2}{25} = \frac{13}{25}<u><em></em></u>

<u><em /></u>

<u><em /></u>

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