Anyone good at probability Can you help me under stand why the answer is the answer. Go through it with me.?

Question

Ok this is my question. The answer to the first section (A) is 7/18. The answer to the section B is 5/18. How do you do that section B ot the question? Can you go through it with me going through the individual steps of getting the answer. My test is in 2 days for my GCSE, I need to be sure I can answer questions like that. Many thanks.
Ok
A fair spinner has six sections of equal size.
One section is blue, two sections are green and three sections are red.
The spinner is spun twice.

(a) Calculate the probability that it lands on the same colour both times. (I know that part).

b) When the spinner lands on a blue section 7 points are scored.
When the spinner lands on a green section 5 points are scored.
When the spinner lands on a red section 3 points are scored.
Calculate the probability of scoring exactly ten points in two spins.

How do you answer it?

Answer 1

If you know how to do part A, you would know how to do part B.

First draw a circle and divide it into 6 equal parts.

A: To calculate the probability same color both times is by multiplication...

blue and blue,
1/6 * 1/6 = 1/36

green and green,
2/6 * 2/6 =4/36

red and red
3/6 *3/6 = 9/36

You need to add up all of these fractions to get the total probability that blue, green, and red is landed on twice.

1/36 + 4/36 + 9/36 = 14/36 and simplifies to 7/18

B: On the same diagram, put numbers to the colors as the instructions tell you: blue = 7, green = 5, and red = 3

What are the different combinations you can have the colors land on to create 10?

7+3: blue, red = 1/6 *3/6 = 3/36
5+5: green, green = 2/6 *2/6 = 4/36
3+7: red, blue = 3/6 * 1/6 = 3/36

you still have to add them all up

3/36 + 4/36 + 3/36 = 10/36 which simplifies to 5/18

Answer 2

The only ways to score 10 points in two spins is in table:
1-st spin score/prob second spin score/prob
7 with prob 1/6 and 3 with prob 3/6 => prob = 3/36
3 with prob 3/6 and 7 with prob 1/6 => prob = 3/36
5 with prob 2/6 and 5 with prob 2/6 => prob = 4/36

If you now sum up right probabilities you get 10/36 = 5/18.

Answer 3

this is done as per enumaration

how do you get 10 points(7+3 or 3+ 7 or 5+ 5)

1) 1st one bule second one red = 1/6*3/6= 36
2) 1st one red second one bule 3/18
3) both are green 2/6*2/6= 4/36

total probability = 3/36+3/36+4/36 = 10/36 or 5/36