Suppose that A and B are independent events such that P(A)=0.10 and P(B¯)=0.20 Find P(A∩B) and P(A∪B)

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Suppose that A and B are independent events such that P(A)=0.10 and P(B¯)=0.20  Find P(A∩B) and P(A∪B)

wheezym · Accepted Answer

Step 1  The value of P(A∩B) is obtained below:  From the given information, the events A and B are independent events and the probability values are  P(A)=0.10, and the value of P(B) is,  P(B)=1−P(B¯)  =(1−0.20)  P(B)=0.80  The required probability is,  P(A∩B)=P(A)×P(B)  =0.10×0.80  =0.08  The value of P(A∩B) is 0.08  The value of P(A∩B) is obtained by taking the product of probability of event A and the probability of event B. It can be expected that 2% of the event A and B occurs.  Step 2  The value of P(A∪B) is obtained as shown below:  The probability is,  P(A∪B)=P(A)+P(B)−P(A∩B)  =0.10+0.80−0.08  =0.90−0.08  =0.82  The value of P(A∪B) is 0.82.  The value of P(A∪B) is obtained by adding the individual probabilities and then subtracting the probability of A and B to the resulted value. It can be expected that about 82% of times event A or B happens.

Suppose that A and B are independent events such that P(A)=0.10 and P(\bar{B})=0.20 Find P(A\cap B) and P(A\cup B)

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