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Nataly [62]
3 years ago
13

Yahoo creates a test to classify emails as spam or not spam based on the contained words. This test accurately identifies spam (

if it is actually spam) 95% of the time. On the other hand, if an email isn't spam, the test will incorrectly classify it as spam 5% of the time. The prevalence of spam emails is 3 in 10.i) What's the probability that an email picked at random is spam? What's the probability that an email picked at random isn't spam?ii) If you test an email and it reports positive for spam, what is the probability that it is spam? Show your work.iii) If you test an email and it reports negative for spam, what is the probability that it is spam? Show your work.
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
8 0

Answer and Step-by-step explanation:

The computation is shown below:

Let us assume that

Spam Email be S

And, test spam positive be T

Given that

P(S) = 0.3

P(\frac{T}{S}) = 0.95

P(\frac{T}{S^c}) = 0.05

Now based on the above information, the probabilities are as follows

i. P(Spam Email) is

= P(S)

= 0.3

P(S^c) =  1 - P(S)

= 1 - 0.3

= 0.7

ii. P(\frac{S}{T}) = \frac{P(S\cap\ T}{P(T)}

= \frac{P(\frac{T}{S}) . P(S) }{P(\frac{T}{S}) . P(S) + P(\frac{T}{S^c}) . P(S^c) }

= \frac{0.95 \times 0.3}{0.95 \times 0.3 + 0.05 \times 0.7}

= 0.8906

iii. P(\frac{S}{T^c}) = \frac{P(S\cap\ T^c}{P(T^c)}

= \frac{P(\frac{T^c}{S}) . P(S) }{P(\frac{T^c}{S}) . P(S) + P(\frac{T^c}{S^c}) . P(S^c) }

= \frac{(1 - 0.95)\times 0.3}{ (1 -0.95)0.95 \times 0.3 + (1 - 0.05) \times 0.7}

= 0.0221

We simply applied the above formulas so that the each part could come

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Darrel has 36 daisies and 54 roses. He wants to put an equal number of daisies and roses into vases. What is the GREATEST number
castortr0y [4]

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18 number of daisies and 18 number of roses

Step-by-step explanation:

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Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36

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Charlie bought 40 oz of flour for his bakery. He used 18.3 oz to make a loaf of bread, and 0.95 oz for each muffin. How many muf
Furkat [3]

Division is one of the four fundamental arithmetic operations. With the leftover flour of 7.45oz, charlie can make approximately 8 muffins.

<h3>What is Division?</h3>

The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.

A.) The total flour Charlie has was 40 oz, out of this he used 18.3 oz of flour. The amount of flour left now would be 21.7 (40-18.3).

Since a single muffin uses 0.95 oz of flour, therefore, the number of muffins Charlie made will be,

Number of muffins = 21.7/0.95 = 22.84 ≈ 23 muffins

B.) When Charlie had 7.45 oz of flour leftover, then the number of muffins would be,

Number of muffins = 7.45/0.95 = 7.84 ≈ 8 muffins

Hence, with the leftover flour of 7.45oz charlie can make approximately 8 muffins.

Learn more about Division:

brainly.com/question/369266

#SPJ1

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