A positive integer from one to six is to be chosen by casting a die. Thus the elements c of the sample space C are 1, 2, 3, 4, 5, 6. Suppose C1 = {1, 2, 3, 4} and C2 = {3, 4, 5, 6}. If the probability set function P assigns a probability of 1 6 to each of the elements of C, compute P(C1), P(C2), P(C1 ∩ C2), and P(C1 ∪ C2).

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lublana lublana · Answer 1 · 2019-09-13T19:58:05+02:00

Answer with Step-by-step explanation:

We are given that six integers 1,2,3,4,5 and 6.

We are given that sample space

C={1,2,3,4,5,6}

Probability of each element=[tex]\frac{1}{6}[/tex]

We have to find that [tex]P(C_1),P(C_2),P(C_1\cap C_2) \;and\; P(C_1\cup C_2)[/tex]

Total number of elements=6

[tex]C_1[/tex]={1,2,3,4}

Number of elements in [tex]C_1[/tex]=4

[tex]P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}[/tex]

Using the formula

[tex]P(C_1)=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]C_2[/tex]={3,4,5,6}

Number of elements in [tex]C_2[/tex]=4

[tex]P(C_2)=\frac{4}{6}=\frac{2}{3}[/tex]

[tex]C_1\cap C_2[/tex]={3,4}

Number of elements in [tex](C_1\cap C_2)=2[/tex]

[tex]P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}[/tex]

[tex]C_1\cup C_2=[/tex]{1,2,3,4,5,6}

[tex]P(C_1\cup C_2)=\frac{6}{6}=1[/tex]