SOLUTION: A circular spinner has a blue sector with a centra angle of 72 degrees, a green sector with 144 degree angle, a yellow sector with a 36 degree angle and a red sector with a 108 deg

Question 13320: A circular spinner has a blue sector with a centra angle of 72 degrees, a green sector with 144 degree angle, a yellow sector with a 36 degree angle and a red sector with a 108 degree angle. For the described event, give the probablility as a percent.
The spinner is spun twice. It lands on red, then green. ____12%____
The spinner is spun twice. It lands on red once, and green once. _____12%____
Let A be the event that the spinner lands on green (one spin), and B be the event that it done not land on green.
a. Find P(A)_____ b. Find P(B)______ c. Find P(a not union B). ________
d. Are A and B independent events? ______________

Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
72 degrees is 1/5 of the total of a circle (360)
144 degrees is 2/5.
36 degrees is 1/10
108 degress is 3/10

So,
P(blue) = 0.2
P(green) = 0.4
P(yellow) = 0.1
P(red) = 0.3

--> total is 1, so that is correct.

Now for the questions:
P(red then green)
--> P(red) and P(green)
0.3 * 0.4
0.12
12%

P(once red and once green)
--> P(red then green) OR P(green then red)
0.12 + 0.12
0.24
24%

P(A) = 0.4
P(B) = 1-0.4
--> P(B) = 0.6

P(A union B) means the probability of (A or B), well the spinner has to be green or not green (the definitions of A and B) so, P(A union B) = 1, so P(A not union B) must be 0, ie impossible

As for part d. Event A and event B are mutually exclusive --> if A happens then B cannot.

For 2 events that are mutually exclusive, they cannot be independent.

jon.

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