Answer:
A,D and E
Step-by-step explanation:
Intuitively speaking two events are independents when the occurrence of one event (A) does not exert influence over the event (B)
Symbolic speaking in terms of sets
P(A∩B)= P(A) * P(B)
Examining each alternative
A. Flipping two coins and having one show a head and the other show a head
Independent. Each flipping coin does not exert any influence on the other
B. Being sneezed on and catching a cold
Dependent. This sequence of events expresses cause consequences effects.
C. When rolling a pair of dice, getting a total of 6 and having one die show a 3
Dependent
Under these conditions, the second event is dependent since all we need is a sum of six, having the first dice showing three. The second one has to show three. So it does exert influence under the result.
D. Rolling a 4 on one die and rolling a 2 on another die
Independent. To get a 4 does not exert any influence on getting a 2 on another dice.
E. Seeing clouds and winning the lottery
Independent.
There is no influence seeing clouds and winning the lottery.
