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ASHA 777 [7]
3 years ago
5

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).
Mathematics
1 answer:
Alex_Xolod [135]3 years ago
4 0

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=\frac{1}{6}

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

Total number of elements=6

C_1={1,2,3,4}

Number of elements in C_1=4

P(E)=\frac{number\;of\;favorable \;cases}{Total;number \;of\;cases}

Using the formula

P(C_1)=\frac{4}{6}=\frac{2}{3}

C_2={3,4,5,6}

Number of elements in C_2=4

P(C_2)=\frac{4}{6}=\frac{2}{3}

C_1\cap C_2={3,4}

Number of elements in (C_1\cap C_2)=2

P(C_1\cap C_2)=\frac{2}{6}=\frac{1}{3}

C_1\cup C_2={1,2,3,4,5,6}

P(C_1\cup C_2)=\frac{6}{6}=1

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