Question

Three coins are tossed once. Let A denote the event “three tails show”, B denote the event “one tail and two head show”, C denote the event “tail on the first coin”.
Which pair of events are
Mutually exclusive?
Simple events?
Compound events?

Answer 1

Hint: Mutual, simple, and compound are three events that we need to understand carefully. We will compare events A, B, and C separately with each other and determine which of the following pairs gives us Compound, Simple and mutual events accordingly.
All three events give us tails. But the difference in each event is that the first even A shows all three coins as tails. The second has one tail and two heads but we can not determine which coin will have the tails. The third event shows that the first coin should be tails.

Complete step-by-step answer:
The events A and B are mutually exclusive since event A tells us that the event shows three tails meaning that all the coins tossed will have tails. Whereas even B shows that one tail will arise and two heads will arise. They contradict each other because there can either be all three tails coin acquired or there can be one tail and two heads coined acquired.

Events C and A are simple events. Since we have been told that event A will show all three coins as tails we know that the 1st,2nd and 3rd coins will all have tails and from event C we have been told that the 1st coin should be tails. Thus, they do not contradict each other making these two events simple events.

Event C and event B are Compound events. These two are compound events because we have been told through event C that the first coin shows tails but event B says that the coins will show one tail and two heads. Though, both the events show one tail it is not specified in event B which coin will have the tails shown. The coin which shows tails can be 1st or in 2nd or 3rd, so, we will have to calculate all the probability thus making this pair of an event as compound events

Note: Mutually exclusive events means that two events can’t happen simultaneously. We can either turn right or we can turn left. We can’t do both. Thus, events A and B being mutually exclusive events.
Simple events can be considered when two events are not in contradiction with each other or when they have equal probability value.
The compound event here is the most complex one with many other possibilities. Same in event C and B where there can be many outcomes for tails coming in event B as a comparison to event C.