Consider an experiment: Two marbles are drawn at random and without replacement

Question

Consider an experiment: Two marbles are drawn at random and without replacement from a box containing two blue marbles, B_1 and B_2, and three red marbles, R_1, R_2, and R_3. List all possible sample points for this experiment. Identify the sample points included in A:= {Two blue marbles are drawn} and compute P (A) Identify the sample points included in B:= {A red and a blue marble are drawn} and compute P(B) Identify the sample points included in C:= {Two red marbles are drawn} and compute P (C)

Explanation / Answer

Blue Marbles : B1,B2 :

Red Marbles : R1,R2,R3

(a). All possible sample points for this experiment :(When two marbles are drawn)

(B1,B2), (B1,R1), (B1,R2), (B1,R3), (B2,R1), (B2,R2), (B2,R3), (R1,R2), (R1,R3), (R2,R3)

Number of all possible sample points = 10

(b) Indentify the sample points included in A:= {Two Blue marbles drawn)

the sample points included in A:= {Two Blue marbles drawn} = (B1,B2)

Number of sample points for A = 1

P(A) = Number of sample points for A / Number of all possible sample points = 1/10

P(A) = 0.1

(c)

Indentify the sample points included in B:= {A red Marble and a Blue marble drawn}

the sample points included in B:= {A red Marble and a Blue marbles drawn} = (B1,R1), (B1,R2), (B1,R3), (B2,R1), (B2,R2), (B2,R3)

Number of sample points for B = 6

P(B) = Number of sample points for B / Number of all possible sample points = 6/10 = 0.6

P(B) = 0.6

(d)

(b) Indentify the sample points included in C:= {Two Red marbles drawn)

the sample points included in C:= {Two Red marbles drawn} = (R1,R2), (R1,R3), (R2,R3)

Number of sample points for C = 3

P(C) = Number of sample points for C / Number of all possible sample points = 3/10= 0.3

P(C) = 0.3

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