Question

Which of the following are independent pairs of events? Check all that apply.

A. Flipping two coins and having one show a head and the other show a head
B. Being sneezed on and catching a cold
C. When rolling a pair of dice, getting a total of 6 and having one die show a 3
D. Rolling a 4 on one die and rolling a 2 on another die
E. Seeing clouds and winning the lottery

Answer 1

Independent events are exclusive or non-mutual events that when one event happens, its occurrence does not affect the occurrence of the other event. in this case, A could be a case. Also, options D  and E could be another case of independent events 

Answer 2

A,D and E

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.