1. ## space diagram

can someone help and tell me that ive done it right?

Two spinning tops are made using square pieces of cardboard with
matchsticks through the centre. One spinner has numbers 1, 2, 3, 4 on
each side of the square and the second spinner is made with numbers
5, 6, 7, 8. Draw a sample space diagram of all the outcomes of
spinning both tops. What is the probability that

(a) at least one number is odd
(b) the 2 numbers added together is 10

this is my solution....

(1st spin)

[1][2][3][4]
-------------
15 25 35 45 |5 (2nd spin)
16 26 36 46 |6
17 27 37 47 |7
18 28 38 48 |8

from the above diagram.

(a) 12/16 (at least one number is odd)
(b) 3/16 ( 2 numbers add up to ten)

2. (b) is correct. (a) is not.

(a)

spinner 1 {1,2,3,4} probability of getting an odd number is $\frac{2}{4}$
spinner 2 {5,6,7,8}probability of getting an odd number is $\frac{2}{4}$

x= the number of odd numbers

$pr(x\geq 1) = pr(x=1)+pr(x=2)$

pr(x=1)= [pr(spinner1 has odd number)*pr(spinner2 does not have odd number)]+pr(spinner2 has odd number)*pr(spinner1 does not have odd number)]

$pr(x=1)=[(\frac{2}{4})(\frac{2}{4})]+[(\frac{2}{4})(\frac{2}{4})]=\frac{1}{2}$

pr(x=2)=pr(spinner1 AND spinner2 both have odd numbers)

$pr(x=2)=(\frac{2}{4})(\frac{2}{4})=\frac{1}{4}$

Therefore,

$pr(x\geq 1)=\frac{1}{2} + \frac{1}{4}=\frac{3}{4}$

Oops! I should learn to read. Both are correct!