Respuesta :
The probability is 0.3, or 30%.
These are not independent events; one pill being chosen will affect the probability after that, as the pill will not be replaced before selecting the next one.
The probability of getting exactly 1 narcotic pill is given by:
(6/15)(9/14)(8/13) = 432/2730. It does not matter what order the narcotic pill is in, the overall product will be the same.
The probability of getting exactly 2 narcotic pills is given by:
(6/15)(5/14)(9/13) = 270/2730. Again, the order these are found in does not matter, as it is multiplication and will not change the product.
The probability of all 3 pills being narcotics is given by:
(6/15)(5/14)(4/13) = 120/2730.
Adding these three possibilities together, we have 822/2730 = 0.30.
These are not independent events; one pill being chosen will affect the probability after that, as the pill will not be replaced before selecting the next one.
The probability of getting exactly 1 narcotic pill is given by:
(6/15)(9/14)(8/13) = 432/2730. It does not matter what order the narcotic pill is in, the overall product will be the same.
The probability of getting exactly 2 narcotic pills is given by:
(6/15)(5/14)(9/13) = 270/2730. Again, the order these are found in does not matter, as it is multiplication and will not change the product.
The probability of all 3 pills being narcotics is given by:
(6/15)(5/14)(4/13) = 120/2730.
Adding these three possibilities together, we have 822/2730 = 0.30.
The probability that the traveler will be arrested for illegal possession of narcotics [tex]\boxed{0.738}.[/tex]
Further Explanation:
The formula of permutation can be expressed as,
[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]
Here, “n” represents the total observations and “r” represents number of the observation has to be arranged.
Given:
There are 6 narcotic tablets in a bottle.
There are 9 vitamin tablets in a bottle.
Explanation:
The total number of tablets are [tex]15{\text{ tablets}}.[/tex]
The probability of getting a narcotic tablet is [tex]\dfrac{2}{5}.[/tex]
The probability of getting a vitamin tablet is [tex]\dfrac{3}{5}.[/tex]
The probability that the traveler will be arrested for illegal possession of narcotics can be obtained as follows,
[tex]\begin{aligned}{\text{Probability}} &= {}^3{C_1}{\left( {\frac{2}{5}} \right)^1}{\left( {\frac{3}{5}} \right)^2} + {}^3{C_2}{\left( {\frac{2}{5}} \right)^2}\left( {\frac{3}{5}} \right) + {}^3{C_3}{\left( {\frac{2}{5}} \right)^3}\\&= 0.432 + 0.288 + 0.018\\&= 0.738\\\end{aligned}[/tex]
The probability that the traveler will be arrested for illegal possession of narcotics [tex]\boxed{0.738}.[/tex]
Learn more:
- Learn more about normal distribution https://brainly.com/question/12698949
- Learn more about standard normal distribution https://brainly.com/question/13006989
- Learn more about confidence interval of meanhttps://brainly.com/question/12986589
Answer details:
Grade: College
Subject: Statistics
Chapter: Binomial Distribution
Keywords: detection, customs, traveler, places, 6 narcotic, narcotic tablets, bottle, vitamin, 9 vitamin tablets, similar, customs, official, selects, illegal possession, arrested, traveler, random analysis, probability, narcotics.
