One urn, U1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn, U2, contains two red balls (labeled R4 and R5) and two blue balls (labeled B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement. (a) Construct the possibility tree showing all possible outcomes of this experiment.

One urn, U1, contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn, U2, contains two red balls (labeled R4 and R5) and two blue balls (labeled B2 and B3). An experiment is performed in which one of the two urns is chosen at random and then two balls are randomly chosen from it, one after the other without replacement.

a. Construct the possibility tree showing all possible outcomes of this experiment.

b. What is the total number of outcomes of this experiment?

c. What is the probability that two red balls are chosen?

Step-by-step explanation:

Consider the following

An urn contains one blue ball B₁

and three red balls (R₁, R₂ and R₃)

Second urn contains two red balls (R₄ and R₅) and two blue balls (B₂ and B₃)

An experiment is performedd in which one of the two urns is chosen from it, one after the other without replacement

a. We are to construct the possibility tree that contains all possible outcome  of this experiment

b. We are to find the total number of outcome of this experiment

The total outcome of this experiment are the following

Urn 1 and Urn 2

B₁R₁     B₂B₃

B₁R₂     B₂R₄

B₁R₃     B₂R₅

R₁B₁     B₃B₂

R₁R₂     B₃R₄

R₁R₃     B₃R₅

R₂B₁     R₄B₂

R₂R₁     R₄B₃

R₂R₃     R₄R₅

R₃B₁     R₅B₂

R₃B₁     R₅B₂

R₃B₁     R₅B₂

R₃R₁     R₅B₃

R₃R₂     R₅R₄

There are 24 total possible outcome

c. We are to find the probability that two red balls are chosen

Probability

If S is a finite sample space in which all outcomes are equally likely and E is and event in S then the probability of E, denoted P(E) is as follows

P(E) = The number of successful outcomes in E / The number of outcomes in S

The chosen two balls are red

Out of the 24 outcomes the outcomes in which both are red are as follows

R₁R₂, R₁R₃, R₂R₁, R₃R₁, R₃R₂, R₄R₅, R₃R₄ and R₂R₃

The probability that the two balls chosen are red is as follows P(E) = 8/24

      = 1/3

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