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miv72 [106K]
3 years ago
5

We have two urns. The first urn contains two balls labeled 1 and 2. The second urn contains three balls labeled 3, 4, and 5. We

choose one of the two urns at random with equal probability and then sample one ball, uniformly at random, from the chosen urn. What is the probability that we picked the ball labeled 5
Mathematics
2 answers:
Furkat [3]3 years ago
7 0

Answer:

1 over 7

Step-by-step explanation:

nasty-shy [4]3 years ago
5 0

The probability of picking the urn with the number 5 in it is 1 out of 2, which is written as 1/2.

The probability if picking the number 5 out of that urn would be 1 out of 3 , written as 1/3.

The probability of both is found by multiplying the two probabilities together:

1/2 x 1/5 = 1/10 probability.

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Answer:

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Step-by-step explanation:

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3 years ago
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The sum of four consecutive integers is 418. Find them.
cupoosta [38]

Answer: 103, 104, 105, and 106

Step-by-step explanation: This problem states that the sum of 4 consecutive integers is 418 and it asks us to find the integers.

First represent your 4 consecutive integers as follows.

X ⇒ first integer

X + 1 ⇒ second integer

X + 2 ⇒ third integer

X + 3 ⇒ fourth integer

Since their sum is 418, our equation reads

x + (x + 1) + (x + 2) + (x + 3) = 418.

Simplifying on the left side we get 4x + 6 = 418.

Now we can subtract 6 from both sides of the equation and we have

4x = 412.

Now just divide both sides by 4 and we find that <em>x = 103</em>.

Finally, make sure you list all your answers.

If <em>x</em> is 103, then <em>x </em>+ 1 is 104, <em>x</em> + 2 is 105, and <em>x</em> + 3 is 106

Therefore, our 3 consecutive integers are 103, 104, 105, and 106.

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Find all solutions in the interval [0,2pi).<br> 2sin^2(x)=sin(x)
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2\sin^2 x  =\sin  x \\\\\implies 2 \sin^2 x -  \sin x=0\\\\\implies \sin x(2 \sin x -1) =0\\\\\implies \sin x =  0~~\text{or}~~ 2 \sin x -1 =0\\\\\implies \sin x = 0~~ \text{or}~ ~ \sin x = \dfrac 12\\\\\text{For}~~ \sin x = 0\\\\x=n\pi \\\\\text{In the interval,}~~[0, 2\pi)\\\\x=0, \pi\\\\\text{For}~~ \sin x = \dfrac 12\\\\x=n\pi+(-1)^n \dfrac{\pi}6 \\\\\text{In the interval,}~~[0, 2\pi)\\\\x=\dfrac{\pi}6,~ \dfrac{5\pi}6\\\\\text{Hence,}~ x = 0,~\pi,~ \dfrac{\pi}6, ~\dfrac{5 \pi}6

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2 years ago
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