Question

Darnell is selecting names from a hat to determine who will choose the family activities for the weekend. The names in the hat include his mother, father, sister, and him. Calculate the probability of each compound event.
P (Darnell and Sister),with replacementP (Mother and Father),without replacement
P (Parent and sister),without replacementP (Parent and child),with replacement
A. 1/6B. 1/16C. 1/4D. 1/12

Answer 1

@KingGeorge can you help me please?

Answer 2

For the first one, there are two ways to do it.

1: Darnell is picked and then Sister.
2: Sister is picked and then Darnell.

Each way has exactly \[\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}\]chance of happening. Thus your total probability should be \[2\cdot\frac{1}{16}=\frac{1}{8}\]But that doesn't seem to be an option...

Answer 3

Okay. well can you help with the rest? and thank you so much for that answer :)

Answer 4

I've got time to help you with one of them, but then I need to go. Hopefully I'll have given you enough of an idea so that you can finish them.

Answer 5

thank you for stopping by, and i will try to finish them. thankss:)

Answer 6

Let's do the second one.

P(Mother and Father), without replacement.

Once again, 2 ways to do this. Mother then Father, or Father then Mother. Both ways have equal probability. The probability of Mother then Father will be\[\frac{1}{4}\cdot\frac{1}{3}=\frac{1}{12}\]Since we have 4 other people at first, but since there's no replacement, there are only 3 names to choose from afterwards. Since there are two ways to do this, we see that the final solution is \[2\cdot\frac{1}{12}=\frac{1}{6}\]

Answer 7

thank youu :)