You spin the spinner twice. draw a tree diagram and list sample spaces to show the possible outcomes. From that answer questions 1,2 and 3.

The spinner is 4 equal parts for a, b, c ,d
I know the tree diagram- you Have a,b,c,d, and from each of those letters ex. A has four lines so a,b,c,d comes off of the a. do this for each.
sample space:
aa ca
ab cb
ac cc
ad cd
ba da
bb db
bc dc
bd dd
the question I need help on is:
1. P(vowel, b or d)=
I got 1/8 by mult. 1/4*8/16=4/32=1/8

Is this correct?
2. p(a,c)=1/16 which I know is correct
3.P(same letter)=4/16=1/4, which I know is correct
Is the first part correct?
thanks for your help.
Sorry the question was so long

Yes, your calculation for question 1 is correct. Let me explain in more detail how you arrived at the answer.

To find the probability of getting a vowel and either "b" or "d", you correctly multiplied the individual probabilities of each event.

The probability of getting a vowel is 1/4 since there are 4 equal parts on the spinner and one of them is labeled with a vowel.

The probability of getting either "b" or "d" is 2/4 since there are 2 out of 4 equal parts labeled with either "b" or "d".

To find the probability of both events happening together, you multiplied 1/4 (for the vowel) by 2/4 (for "b" or "d").

1/4 * 2/4 = 2/16 = 1/8

So, the probability of getting a vowel and either "b" or "d" is indeed 1/8.

For question 2, you correctly stated that the probability of getting "a" and "c" together is 1/16.

For question 3, you correctly stated that the probability of getting the same letter twice is 4/16, which simplifies to 1/4.

Overall, your answers are correct. Great job!