Determine whether the events are mutually exclusive. When a quarter is tossed fo

Question

Determine whether the events are mutually exclusive.

When a quarter is tossed four times, 16 outcomes are possible.

HHHH HHHT HHTH HHTT
HTHH HTHT HTTH HTTT
THHH THHT THTH THTT
TTHH TTHT TTTH TTTT

Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. The events A and B are defined as follows.

A = event exactly two heads are tossed
B = event all four tosses come up the same

Are the events A and B mutually exclusive?

Yes

No

Yes

No

Explanation / Answer

Mutually exclusive events are those such that if 1 event occurs the other cannot occur. If we want exactly 2 tosses to be heads, then we have the following HHTT, TTHH, HTHT, THTH and if all four tosses come up the same, then we have HHHH or TTTT.

We see that there is no case where the 2 events can happen simultaneously, and hence YES, the 2 events A and B are mutually exclusive.

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