Answer:
Tossing a coin twice; A ={no Heads}, B={at least 1 Head}
Step-by-step explanation:
Mutually exclusive:
If two events are mutually exclusive, if one events happen, the other cannot happen, and vice-versa.
Rolling a die; A={Rolling an even number}, B={Rolling a number greater than 4}
A die has the following outcomes: 1,2,3,4,5,6
Even numbers: 2,4,6
Greater than 4: 5, 6
6 is an outcome of both events A and B, so they are not mutually exclusive.
Picking a card; A= {Selecting a 7}, B={Selecting a Heart}
Cards numbered from 1 to 13, each number with 4 types. So we can have a card of hearts numbered 7, which means that these events are not mutually exclusive.
Tossing a coin twice; A ={no Heads}, B={at least 1 Head}
If you get no heads, the probability of at least 1 head is 0.
If you get at least 1 head, the probability of no heads is 0.
This means that this is the answer, that is, these events are mutually exclusive.
Rolling two 6-sided dice; A={rolling a sum of 4}, B={rolling a 3 on one die}
(3,1) or (1,3) has a sum of 4 and a 3 on one die, which means that these events are not mutually exclusive.
