Question

(adapted from Ross, 2.31) Three countries (the Land of Fire, the Land of Wind, and the Land of Earth) each make a 3 person team. Each team consists of three ninjas, each of a different rank: one genin junior ninja, one journeyman ninja, and one elite ninja.
(a) If a ninja is chosen at random from each of the three different countries, what is the probability of selecting a complete team? (A complete team here is a group consisting of three ninjas, each ninja of a different rank).

(b) If a ninja is chosen at random from each of the three different countries, what is the probability that all 3 ninjas selected have the same rank?

Answer 1

Answer:

The answer is "$\frac{2}{9} \ and \ \frac{1}{9}$"

Step-by-step explanation:

In point a:

The requires  1 genin, 1 chunin , and 1 jonin to shape a complete team but we all recognize that each nation's team is comprised of 1 genin, 1 chunin, and 1 jonin.

They can now pick 1 genin from a certain matter of national with the value:

$\frac{1}{\binom{3}{1}}=\frac{1}{3} .$

They can pick 1 Chunin form of the matter of national with the value:

$\frac{1}{\binom{3}{1}}=\frac{1}{3} .$

They have the option to pick 1 join from of the country team with such a probability: $\frac{1}{\binom{3}{1}}=\frac{1}{3}$

And we can make the country teams: $3! = 6$ different forms. Its chances of choosing a team full in the process described also are:

$6 \times \frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}=\frac{2}{9}.$

In point b:

In this scenario, one of the 3 professional sides can either choose 3 genins or 3 chunines or 3 joniners. So, that we can form three groups that contain the same ninjas (either 3 genin or 3 chunin or 3 jonin).

Its likelihood that even a specific nation team ninja would be chosen is now: $\frac{1}{\binom{3}{1}}=\frac{1}{3}$

Its odds of choosing the same rank ninja in such a different country team are: $\frac{1}{\binom{3}{1}}=\frac{1}{3}$

The likelihood of choosing the same level Ninja from the residual matter of national is: $\frac{1}{\binom{3}{1}}=\frac{1}{3}$ Therefore, all 3 selected ninjas are likely the same grade: $3\times \frac{1}{3}\times \frac{1}{3}\times \frac{1}{3}=\frac{1}{9}$

Answer 2

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Step-by-step explanation: