another spinner prob

Mar 2010
110
0
A circular spinner has 8 equally spaced spots; there are 3 blue, 2 green, 2 yellow and 1 red space. Let events A and B be defined as follows:
A = {outcomes with a blue on the first spin}
B = {outcomes with yellow on a spin}

Find:
a.) probability (A)

b.) probability (B)

c.)probability (A union B)

I have questions about all 3:
a.) would this just be 3/8, or do i need to factor in the second spin

b.) would this be 1/64 = 1/8 * 1/8

c.) what exactly is this part asking? prob(blue followed by a yellow)??? and if so would this just be 3/8 * 1/8 = 3/64?
 

matheagle

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Feb 2009
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It looks like you are spinning the wheel twice.
But who knows.
A is 3/8 no matter how many spins
Do you want exactly two or at least one yellow in B?
 
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Mar 2010
110
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oops, that's my bad...the spinner is spun twice and its b = {outcomes with yellow on a spin}, so i am assuming that means at least one yellow

sorry
 

matheagle

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Feb 2009
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oops, that's my bad...the spinner is spun twice and its b = {outcomes with yellow on a spin}, so i am assuming that means at least one yellow

sorry
Instead of looking at the event of at least one yellow.
Use the complement, no yellow...1-(3/4)(3/4).
 
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Mar 2010
110
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ok thanks that makes sense
so the probability of yellow on a spin would look like this:

n(s) = 8*8 =64
n(no yellow) = 6*6 =36
n(a yellow) = 28

prob(no yellow) = 36/64 = 9/16
prob(outcomes of yellow on a spin) = 28/64 = 7/16


then for the last part...what does a union b mean. does that mean a then b?
 
May 2010
3
0
Union means both A and B occur. With the events in this example, this basically means the event that you get a blue first, then a yellow, so in this case it does mean A then B, but this wouldn't always be the case. I believe the probability you calculated is correct.
 

matheagle

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Feb 2009
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Union means both A and B occur. With the events in this example, this basically means the event that you get a blue first, then a yellow, so in this case it does mean A then B, but this wouldn't always be the case. I believe the probability you calculated is correct.

sorry
union is an or
intersection is an and, meaning BOTH sets must occur.
 
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Mar 2010
110
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so A u B means A or B, or A and B?

if so does this mean (3/8) + (7/16) + (3/8)*(7/16)
 

matheagle

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Feb 2009
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\(\displaystyle P(A\cup B)=P(A)+P(B)-P(AB)\)

where \(\displaystyle AB\) is the intersection of A and B.

The event \(\displaystyle AB\) means BOTH must occur

While \(\displaystyle A\cup B\) means at least one must occur, maybe both.
 
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Mar 2010
110
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so would 3/8 + 7/16 - P(AB) be correct?

and for P(AB) would I just multiply (3/8)(1/4)? that being 3/8 prob of blue on 1st spin and (1/4) prob of yellow on the second spin

thanks for your help