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Snowcat [4.5K]
4 years ago
14

A spinner has 10 equally sized sections, 5 of which are gray and 5 of which are blue. The spinner is spun twice. What is the pro

bability that the first spin lands on gray and the second spin lands on blue? Write your answer as a fraction in the simplest form.
Mathematics
1 answer:
vampirchik [111]4 years ago
3 0

Answer:

<h2>1/4</h2>

Step-by-step explanation:

Probability is the likelihood or chance that an event will occur. Mathematically,

Probability = Expected outcome/Total outcome

If the spinner has 10 equally sized sections 5 of which are gray and 5 of which are blue, the total outcome will be equal to 10.

The probability that spinning lands on blue = 5/10

The probability that spinning lands on gray = 5/10

The probability that the first spin lands on gray and the second spin lands on blue is 5/10*5/10 = 25/100

25/100 = 1*25/(4*25) = 1/4

<em>Hence, the probability that the first spin lands on gray and the second spin lands on blue in its simplest form is 1/4</em>

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Write the left side of the given expression as N/D, where
N = sinA - sin3A + sin5A - sin7A
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Therefore we want to show that N/D = cot2A.

We shall use these identities:
sin x - sin y = 2cos((x+y)/2)*sin((x-y)/2)
cos x - cos y = -2sin((x+y)/2)*sin((x-y)2)

N = -(sin7A - sinA) + sin5A - sin3A
    = -2cos4A*sin3A + 2cos4A*sinA
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    = -4cos4A*cos2A*sinA

D = cos7A + cosA - (cos5A + cos3A)
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Therefore
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This verifies the identity.
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