Question

Two coins are tossed. if a is the event "two heads" and b is the event "two tails", are a and b mutually exclusive? are they complements?

Answer 1

Two coins are tossed. The events A (two heads) and B (two tails) are mutually exclusive but not complements.

Step-by-step explanation:

a. In this question, we are given two events A and B, where A represents the event of getting two heads and B represents the event of getting two tails when two coins are tossed.

For a and b to be mutually exclusive, they should not be able to occur at the same time. Since it is not possible to get both two heads and two tails from the same coin toss, a and b are mutually exclusive.

For events to be complements of each other, their union should cover the entire sample space and their intersection should be an empty set. In this case, A and B do not fulfill these conditions, so they are not complements of each other.

Answer 2

For the first one, yes they are mutually exclusive because:
- If event A happens it is impossible for event B to occur

- If event B happens it is impossible for event A to occur


For the second question, they are not complements.

To be complements the sum of the probabilities of the two events MUST add to 100%. In this situation, if you toss two coins, you can also get ONE head and ONE tail. In short, they are not complements because Event A + Event B do NOT equal 100% of all possible outcomes when tossing two coins.