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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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A body moves s metres in a time t seconds so that s = t3 – 3t2 + 8. Find:
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Using derivatives, it is found that:

i) v(t) = 3t^2 - 6t

ii) 9 m/s.

iii) a(t) = 6t - 6

iv) 6 m/s².

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<h3>What is the role of derivatives in the relation between acceleration, velocity and position?</h3>
  • The velocity is the derivative of the position.
  • The acceleration is the derivative of the velocity.

In this problem, the position is:

s(t) = t^3 - 3t^2 + 8

item i:

Velocity is the <u>derivative of the position</u>, hence:

v(t) = 3t^2 - 6t

Item ii:

v(3) = 3(3)^2 - 6(3) = 27 - 18 = 9

The speed is of 9 m/s.

Item iii:

Derivative of the velocity, hence:

a(t) = 6t - 6

Item iv:

a(2) = 6(2) - 6 = 6

The acceleration is of 6 m/s².

Item v:

t for which a(t) = 0, hence:

6t - 6 = 0

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t = 1

Hence 1 second.

You can learn more about derivatives at brainly.com/question/14800626

7 0
2 years ago
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