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babymother [125]
3 years ago
6

A number is selected, at random, from the set {1,2,3,4,5,6,7,8}.

Mathematics
1 answer:
Olegator [25]3 years ago
5 0

Applying the formula, you have:

A = the number is prime

B = the number is odd

I assume that with "random" you imply that all numbers can be chosen with the same probability. So, we have

P(A) = \dfrac{4}{8} = \dfrac{1}{2}

because 4 out of 8 numbers are prime: 2, 3, 5 and 7.

Similarly, we have

P(B) = \dfrac{4}{8} = \dfrac{1}{2}

because 4 out of 8 numbers are odd: 1, 3, 5 and 7.

Finally,

P(A \land B) = \dfrac{3}{8}

because 3 out of 8 numbers are prime and odd: 3, 5 and 7.

So, applying the formula, we have

P(\text{prime } | \text{ odd}) = \dfrac{P(\text{prime and odd})}{P(\text{odd})} = \dfrac{\frac{3}{8}}{\frac{1}{2}} = \dfrac{3}{8}\cdot 2 = \dfrac{3}{4}

Note:

I think that it is important to have a clear understanding of what's happening from a conceptual point of you: conditional probability simply changes the space you're working with: you are not asking "what is the probability that a random number, taken from 1 to 8, is prime?"

Rather, you are adding a bit of information, because you are asking "what is the probability that a random number, taken from 1 to 8, is prime, knowing that it's odd?"

So, we're not working anymore with the space {1,2,3,4,5,6,7,8}, but rather with {1,3,5,7} (we already know that our number is odd).

Out of these 4 odd numbers, 3 are primes. This is why the probability of picking a prime number among the odd numbers in {1,2,3,4,5,6,7,8} is 3/4: they are literally 3 out of 4.

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4 0
3 years ago
Find the radius. Round to the nearest tenth.
Arlecino [84]

Answer:

Step-by-step explanation:

V = 1/3 * pi * r^2 * h

r = ?

pi = 3.14

h = 17 cm

3*V = pi * r^2 h = r^2    Divide by pi

3*V/pi = r^2 h  = r^2     Divide by h

3*V/(pi*h)         =r^2      Take the square root of the left to get just  r

sqrt(3*V/(pi*h))  = r         Now solve the equation.

sqrt(3*538.25 /(3.14*17)) = r

sqrt(1614 / 53.38) =

r = sqrt(30.24)

r = 5.493

6 0
2 years ago
An angle measures 52° more than the measure of its complementary angle. What is the measure of each angle?
olga2289 [7]
Answer:
First angle is 71, and the other is 19

A complementary angle is 90, so 71 + 19 = 90, while having a 52 degree difference
7 0
3 years ago
15% 40% as whole numbers
Alex17521 [72]

Answer: Not possible

Step-by-step explanation: A whole number is an integer or a number without fractions. Both 15% and 40% are less than 1 since they are less than 100%; therefore, it is impossible to express them as whole numbers. They can only be expressed as the mixed numbers of 0.15 and 0.4, or 15/100 and 40/100.

3 0
3 years ago
Read 2 more answers
Please help!!!! please help!!!!!​
Nata [24]
[True]

Natural numbers are the positive integers (whole numbers) such as 1, 2, 3, and etc. So it is true that zero is less than every natural number.

[Hundreds]

The 8 in 30,846 is in the hundreds place because the 8 stands for 800.
6 0
2 years ago
Read 2 more answers
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