Question

One urn contains one blue ball (labeled $$B_1$$) and three red balls (labeled $$R_1, R_2$$, and $$R_3$$). A second urn contains two red balls ($$R_4$$ and $$R_5$$) and two blue balls ($$B_2$$ and $$B_3$$). 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?

Answer 1

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

see the attached file below

b. WeWe 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