Lester John Sus

2022-05-03

To avoid detection at customs, a traveler places 6 narcotic tablets in a bottle 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 the traveler will be arrested for illegal possession of narcotics?

karton

Expert2022-07-07Added 613 answers

A traveler places narcotic tablets in a bottle with 9 vitamin tablets that are similar in appearance (so, there will be total 6+9=15 tablets in the bottle).

The customs official selects 3 of the tablets at random for analysis.

* We need to find the probability that the traveler will be arrested for illegal possession of narcotics.

The traveler will be arrested if the customs official finds at least 1 narcotic table among 3 randomly selected tablets from the traveler's bottle.

Let random variable X represent the number of narcotic tablets among 3 randomly selected tablets from the traveler's bottle. Therefore, we need to find $P(X\ge 1)$.

Lets consider as a success an event when the customs official finds the narcotic table.

So, we have a random sample of size n=3 (the custom official selects 3 tablets for

analysis), taken from $N=6+9=15$ items (there are 15 tables in the traveler's bottle) of which k=6 are labeled success (there are 6 narcotic tablets in the bottle) and $N-k=15-6=9$ are labeled failure.

Thus, X is hypergeometric random variable.

The probability distribution of hypergeometric random variable X is:

$h(x;N,n,k)=\frac{\left({\displaystyle \frac{k}{x}}\right)\left({\displaystyle \frac{N-k}{n-x}}\right)}{\left({\displaystyle \frac{N}{n}}\right)}$

We need to find

$P(X\ge 1)=1-P(X=0)=1-h(0;15,3,6)\left(1\right)$

According to probability distribution of the hypergeometric random variable X, we

have:

$h(0;15,3,6)=\frac{\left({\displaystyle \frac{6}{0}}\right)\left({\displaystyle \frac{15-6}{3-0}}\right)}{\left(\frac{15}{3}\right)}$

$=\frac{\left({\displaystyle \frac{6}{0}}\right)\left({\displaystyle \frac{9}{3}}\right)}{\left(\frac{15}{3}\right)}=\frac{{\displaystyle \frac{6!}{0!(6-0)!}\frac{9!}{3!(9-3)!}}}{{\displaystyle \frac{15!}{3!(15-3)!}}}$

$=\frac{\left(1\right)\left(84\right)}{455}\approx 0.1846\left(2\right)$

According equations (1) and (2), we get the required probability as follows:

$P(X\ge 1)=1-h(0;15,3,6)=1-0.1846=0.8154$

So, the probability that the traveler will be arrested is 0.8154

At the beginning of an environmental study, ad forest covered an area of $1500k{m}^{2}$.Since then, this area has decreased by 4.25% each year.Let t be the number of years since the start of the study.Let y be the area that the forest covers in $k{m}^{2}$.

Write an exponential function showing relationship between y and t.Some friends tell you that they paid $25,000 down on a new house and are to pay $525 per month for 30 years. If interest is 7.8% compounded monthly, what was the selling price of the house? How much interest will they pay in 30 years?

t e^-4t sin3t

Find all whole number solutions of the congruence equation.

3x ≡ 8 mod 11Use a direct proof to show that the product of two rational numbers is rational.

Y=2(x-) (x+1)

what is vertex

axis of symmetry

x-intercept(s)

y-intercept

Stairs- Each step of a set of stairs has a tread depth of 11.5 inches and a riser height of 6.5 inches. What is the slope of the set of stairs?

A ball of mass 5 kg is attached to a string of length 10 cm, forming a pendulum. If the string is raised horizontally as shown and released from point A, then what is the v

assume that the random variable Xand Y have the joint pdf f(x,y)=1/2x^3

5=20 mod 4 true or false answer

5x−4y=

- $\text{\hspace{0.17em}}\text{\hspace{0.17em}}-12$−12

Pets Plus and Pet Planet are having a sale on the same aquarium. At Pets Plus the aquarium is on sale for 30% off the original price and at Pet Planet it is discounted by 25%.

**Store****Original Price****of Aquarium ($)**Pets Plus 118 Pet Planet 110 If the sales tax rate is 8%, which store has the lower sale price?

, 1 of 1.Select ChoicePets PlusPet Planet has the lower sale price.

**Part B**Fill in the blank question.

How much will you save by buying the aquarium at the store with the lower sale price? Round to the nearest cent.

$

Prove that if x is and irrational number and x>0 then route over x is also irrational

A small object has charge Q. Charge q is removed from it and placed on a second small object. The two objects are placed 1 m apart. For the force that each object exerts on the other to be a maximum. q should be: A. 2Q B. Q C. Q/2 D. Q/4 E. 0