Determine whether the events are mutually exclusive. When a quarter is tossed fo
ID: 3362063 • Letter: D
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 the first two tosses are heads
B = event the first and last tosses are the same
Are the events A and B mutually exclusive?
Yes
No
Yes
No
Explanation / Answer
A = event the first two tosses are heads
B = event the first and last tosses are the same
If the outcome is HHHH, HHTH then
A is true since the first two tosses are heads
B is true since the first and the last tosses are same.
Therefore, it is possible for both A and B to be true.
The events are not mutually exclusive.
The answer is No.
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