Question

PLEASE HELP I WILL GIVE A MEDAL: Suppose the two spinners shown are each spun once. Find the probability that the first spinner lands on a number that is greater than 2 and the sum of the spinners is less than 8.

Answer 1

what is the probability that the number on spinner one is greater than 2 ?

Answer 2

1/4???

Answer 3

i would say \(\frac{1}{2}\) as half the numbers are greater than 2

Answer 4

oh ok

Answer 5

what next?

Answer 6

but we can work in cases if you like
the probability that the first spinner lands on 3 is \(\frac{1}{4}\)

Answer 7

If it lands on a 3, then it doesn't matter what the second spinner lands, the total will definitely be less than 8
that is clear yes?

Answer 8

yeah but I'm still confused about the part that says the sum of the spinners is less than 8. so is it saying the spinner has to be spun more than once?

Answer 9

first the one on the left is spun
it has to be a 3 or a 4
then the one on the right is spun, and the total of the two has to be less than 8

Answer 10

ohh i get it

Answer 11

so lets go slow because although it is easy, the answer might not be obvious

Answer 12

IF the first one land on a 3, then it makes no difference what the second one lands, the total will be less than 8 no matter what
the probability that happens is \(\frac{1}{4}\)
but there is another possibility

Answer 13

the other possibility is that the first spinner lands on a 4, that happens with probability \(\frac{1}{4}\) but then the second spinner has to land on 1 or 2 or 3 but NOT 4
that happens with probability \(\frac{3}{4}\) so the probability that the first spinner is 4 and the second spinner is 1, 2, or 3 is \[\frac{1}{4}\times \frac{3}{4}=\frac{3}{16}\]

Answer 14

to get your answer, add
\[\frac{1}{4}+\frac{3}{16}\]

Answer 15

ok so it would be 7/16

Answer 16

that is what i get, yes
hope the steps were more or less clear

Answer 17

I think i understand thank you so much!

Answer 18

yw

Answer 19

If you wish here is a confirmation of the answer. There are 16 total possibilities.
We can ignore the first 8 as the first spinner is not greater than 2.
In the second 8, we go through each possibility and retriceif the sum is less than 8.

S1 S2 Sum < 8 AND first spinner > 2?
1 1
1 2
1 3
1 4
2 1
2 2
2 3
2 4
-----
3 1 Yes
3 2 Yes
3 3 Yes
3 4 Yes
4 1 Yes
4 2 Yes
4 3 Yes
4 4 No

7 out of 16 possibilities or 7/16

Answer 20

In the second 8, we go through each possibility and ask if the sum is less than 8.

Answer 21

thank you!!