thanks for helping me!
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 answer for question 1 is correct.
Yes, your calculation for question 1 is correct. The probability of getting a vowel and either "b" or "d" can be found by multiplying the probability of getting a vowel (which is 1/4) by the probability of getting "b" or "d" (which is 2/8 = 1/4). This gives you (1/4) * (1/4) = 1/16. Therefore, the correct answer for question 1 is 1/16, not 1/8.
For question 2, you are also correct. The probability of getting "a" followed by "c" can be obtained from the sample space you provided. Since there is only one outcome in the sample space where you get "a" followed by "c" (ac), the probability is 1 out of 16, which can be expressed as 1/16.
For question 3, you are correct again. The probability of getting the same letter twice can be calculated by dividing the number of favorable outcomes (which is 4, as there are 4 options for each letter) by the total number of possible outcomes (which is 16, as there are 4 options for each spin). This gives you 4/16, which simplifies to 1/4.
In summary:
1. P(vowel, b or d) = 1/16
2. P(a, c) = 1/16
3. P(same letter) = 1/4
Well done on your calculations!
The tree diagram and sample spaces you provided are correct. Here's how you can calculate the probabilities for questions 1, 2, and 3:
1. P(vowel, b or d):
To find the probability of getting a vowel (a) and either b or d, you can multiply the individual probabilities. There are two outcomes that satisfy this condition: ab and ad. So the probability is 2/16, which simplifies to 1/8. Therefore, your calculation of 1/8 is correct.
2. P(a, c):
From the sample space, we see that there is only one outcome that satisfies the condition: ac. Since there is only one way to get an ac out of 16 total outcomes, the probability is 1/16. So your calculation of 1/16 is correct.
3. P(same letter):
To find the probability of getting the same letter, we count the number of outcomes where both spins result in the same letter and divide it by the total number of outcomes. From the sample space, we can see that there are four outcomes: aa, cc, bb, and dd. There are a total of 16 outcomes, so the probability is 4/16, which simplifies to 1/4. Therefore, your calculation of 1/4 is correct.
Overall, your answers for questions 1, 2, and 3 are correct. Well done!