  # Let A = {4, 6}, B = {6, 11, 23}, D = {35} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.a) {4, 11, 23}b) {6, 35}c) {6, 11, 23}d) {11, 23}e) {6}f) None of the above.

Question

Let A = {4, 6}, B = {6, 11, 23}, D = {35} and S = sample space = A ∪ B ∪ D. Identify Ac ∩ B.
a) {4, 11, 23}
b) {6, 35}
c) {6, 11, 23}
d) {11, 23}
e) {6}
f) None of the above.

check_circleExpert Solution
Step 1

Given information:

The given events are as follows:

A = { 4, 6 }, B = { 6, 11, 23 }, D = { 35 } and the sample space is S = A B D = { 4, 6, 11, 23, 35 }.

Complement of an event:

Compliment of an event is all outcomes that are not in that event. The union of a particular event and compliment of that event gives all possible outcomes in the sample space for that event.

From the definition of compliment of an event it is known that the event Ac consists of all the elements of the sample space and the elements that are not in A.

The formal notation of the elements of Ac is given below:

Step 2

Find the set of Ac B:

From the definition of compliment of an event, the event Ac ∩ B  consists of elements of B but not the elements of A.

In other words it can be said that, AcB  is B A ∩ B.

The set o...

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### Probability 