Question

The probability that the event A occurs is Pr( A ) = 1/3 and the probability that the union event A∪B occurs is Pr( A∪B ) = 5/6. Answer the following questions.

1. If the events A and B are disjoint, what is the value of Pr(B)?

2. If the events A and B are independent, what is the value of Pr(B)?

(＊Answer in the decimal form, not in the fractional form.)

Thank you so much!

Answer 1

P (A) = 1/3 ; PLAUB) = I P(AUB) = PIADA PCB) – PIANB) A and B are dos joint then Plans Now P(AUB) = PCAS+PCB) & = YztPIB) ) PCB) = [ - = se PIB) = 1/2 = 10.50 A and PIB) 2. B Then indendependet are PlanB) =P( A Now PLAUB) = P(A) + PIC) – P(A). PIB) a = 113 + PIB) – ☆ PIB) PCB8 (17/3) = 55-33 = 2 = 1/2 a Ž PIRE!lz PIB)=4x330175 MJ :P (B) = 0.75