Step 1

The value of \(P(A\cap B)\) 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,

\(P(B)=1-P(\bar{B})\)

\(=(1-0.20)\)

\(P(B)=0.80\)

The required probability is,

\(P(A\cap B)=P(A)\times P(B)\)

\(=0.10\times0.80\)

\(=0.08\)

The value of \(P(A\cap B)\) is \(0.08\)

The value of \(P(A\cap B)\) 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 \(P(A\cup B)\) is obtained as shown below:

The probability is,

\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

\(=0.10+0.80-0.08\)

\(=0.90-0.08\)

\(=0.82\)

The value of \(P(A\cup B)\) is \(0.82\).

The value of \(P(A\cup B)\) 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.

The value of \(P(A\cap B)\) 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,

\(P(B)=1-P(\bar{B})\)

\(=(1-0.20)\)

\(P(B)=0.80\)

The required probability is,

\(P(A\cap B)=P(A)\times P(B)\)

\(=0.10\times0.80\)

\(=0.08\)

The value of \(P(A\cap B)\) is \(0.08\)

The value of \(P(A\cap B)\) 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 \(P(A\cup B)\) is obtained as shown below:

The probability is,

\(P(A\cup B)=P(A)+P(B)-P(A\cap B)\)

\(=0.10+0.80-0.08\)

\(=0.90-0.08\)

\(=0.82\)

The value of \(P(A\cup B)\) is \(0.82\).

The value of \(P(A\cup B)\) 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.