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dexar [7]
3 years ago
8

To avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in

appearance. If the customs official selects 3 of the tablets at random for analysis, what is the probability that that the traveler will be arrested for illegal possession of narcotics?
Mathematics
1 answer:
Alexus [3.1K]3 years ago
6 0

Answer:

\frac{4}{91}

Step-by-step explanation:  

We are told that to avoid detection at customs, a traveler has placed 6 narcotic tablets in an Urn containing 9 vitamin pills that are similar in appearance.

To find the probability that the traveler will be arrested for illegal possession of narcotics we will use theoretical probability formula.

\text{Probability}=\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}

Favorable outcomes will be _{3}^{6}\textrm{C}.

\text{Favorable outcomes}=_{3}^{6}\textrm{C}=\frac{6!}{(6-3)!3!}

\text{Favorable outcomes}=\frac{6!}{3!3!}

\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4\cdot3!}{3\cdot 2\cdot 1\cdot3!}

\text{Favorable outcomes}=\frac{6\cdot 5\cdot 4}{3\cdot 2}

\text{Favorable outcomes}=5\cdot 4=20

Now let us find number of possible outcomes.

\text{Number of possible outcomes}=_{3}^{15}\textrm{C}=\frac{15!}{(15-3)!3!}

\text{Number of possible outcomes}=\frac{15!}{12!3!}

\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13\cdot 12!}{12!\cdot 3\cdot 2\cdot 1}

\text{Number of possible outcomes}=\frac{15\cdot 14\cdot 13}{ 3\cdot 2\cdot 1}

\text{Number of possible outcomes}=5\cdot 7\cdot 13=455

Upon substituting our values in probability formula we will get,

\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{20}{455}

Upon dividing numerator and denominator by 5 we will get,

\text{Probability that the traveler will be arrested for illegal possession of narcotics}=\frac{4}{91}

Therefore, the probability that the traveler will be arrested for illegal possession of narcotics is \frac{4}{91}.  


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Helga [31]

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D

Step-by-step explanation:

We need the formula for arc length (in radians) to solve this problem. The formula is:

s=r \theta

Where

s is the arc length

r is the radius of the circle

\theta is the intercepted angle

In this diagram, we can see that  \theta  is beign intercepted by the big arc with measure 20 cm. So arc length, s, is 20

Also, if we look, we see that the radius is 5 cm, so r = 5

Now, we substitute into formula and find \theta:

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This is given in radians, so \theta is 4 radians

D is the correct answer choice.

6 0
3 years ago
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Evgesh-ka [11]

Weird. A period appears above this... huh.

Answer:

[Th]e cube has a greater value.

Step-by-step explanation:

What the word problem really wants us to get [is ]the question of 'Which is greater, A=6a^2 when 'a' [is] 18 or A=4\pir^2 when r = 9? And here's how to solve that.

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So w[e] know that the cube is 1944 meters cube[d ] in area. But what about the more [f]ormidable sphere? Fo[r] it we need a slightly m[o]re co[m]plicated formula, A=4\pir^2. However, instead of using the real pi I will be rounding to 3.14, since we have no calculator so anything more would take way too long and fry your[ bra]in.

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A=4(3.14)(81) Solve expone[n]ts.

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Now, since I'm sure all of us can count, we know that 1944 is greater than 1017.36. Or in other words, the cube is bigger than the sphere.

And PLEASE don't copy this guys. Make your own iteration. Change it up!

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3 years ago
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vichka [17]

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8 0
3 years ago
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Juli2301 [7.4K]

Answer:

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We simply replace a with -9

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