1..)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

choose the one's that are right

lose the apostrophe in one's, unless you also write event's and coin's and cloud's...

independent events do not affect each other. So, I'd choose A,D,E

The independent pairs of events are:

A. Flipping two coins and having one show a head and the other show a head
D. Rolling a 4 on one die and rolling a 2 on another die

These pairs of events are independent because the outcome of one event does not affect the outcome of the other.

To determine which pairs of events are independent, we need to understand the concept of independent events. Two events are considered independent if the occurrence or non-occurrence of one event does not affect the probability of the other event.

Let's analyze each pair of events:

A. Flipping two coins and having one show a head and the other show a head: These events are independent since the outcome of one coin flip does not affect the outcome of the other coin flip. Therefore, A is a correct answer.

B. Being sneezed on and catching a cold: These events are not independent. Being sneezed on can introduce viruses and increase the likelihood of catching a cold. Therefore, B is not a correct answer.

C. When rolling a pair of dice, getting a total of 6 and having one die show a 3: These events are not independent. The outcome of getting a total of 6 depends on the outcome of each individual die roll. If one die shows a 3, the probability of getting a total of 6 is affected. Therefore, C is not a correct answer.

D. Rolling a 4 on one die and rolling a 2 on another die: These events are independent since the outcome of one die roll does not affect the outcome of the other die roll. Therefore, D is a correct answer.

E. Seeing clouds and winning the lottery: These events are not related or dependent on each other. However, for the purpose of this question, we need to consider whether they are dependent or independent in terms of probability. As seeing clouds has no effect on the probability of winning the lottery, these events can be considered independent. Therefore, E is a correct answer.

In summary, the correct answers are A, D, and E.