If the sample space S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} and the events A = {0, 3, 6, 9}, B = {0, 4, 8}, C = {1, 4, 7}, find (a) 𝐴 (b) 𝐴 ∩ 𝐵 (c) 𝐴 ∪ 𝐵 (d) Are the events A and C disjoint?
Added by Heather B.
Step 1
Step 1: Identify the sets: - S = {0,1,2,3,4,5,6,7,8,9} - A = {0,3,6,9} - B = {0,4,8} - C = {1,4,7} Show more…
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Let the sample space {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} for a random experiment be the numbers delineating events A, B, and C through 10. Event A: {1, 4, 5, 7, 9}, Event B: {2, 3, 6, 8}, and Event C: {1, 2, 3, 4, 5}. (a) What outcomes are in the event A and B? (b) What outcomes are in the event C and B? (c) What outcomes are in the event A and B, and B and A? (d) Are the events B and C disjoint?
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Given that the sample space consists of the following outcomes {1,2,3,4,5,6,7,8,9,10} and the event A={1,3,5,7} and B={2,3, 4,6,8}. Find the following: a) (A or B)= b) (A and B)= c) (A and B)= d) (A or B) =
Pritesh R.
Suppose that we have a sample space $S=\left\{E_1, E_2, E_3, E_4, E_5, E_6, E_7\right\}$, where $E_1, E_2, \ldots, E_7$ denote the sample points. The following probability assignments apply: $P\left(E_1\right)=.05, P\left(E_2\right)=20, P\left(E_3\right)=.20, P\left(E_4\right)=.25, P\left(E_5\right)=.15, P\left(E_6\right)=.10$, and $P\left(E_7\right)=05$. Let $$ \begin{aligned} & A=\left\{E_1, E_4, E_6\right\} \\ & B=\left\{E_2, E_4, E_7\right\} \\ & C=\left\{E_2, E_3, E_5, E_1\right\} \end{aligned} $$ a. Find $P(A), P(B)$, and $P(C)$. b. Find $A \cup B$ and $P(A \cup B)$. c. Find $A \cap B$ and $P(A \cap B)$. d. Are events $A$ and $C$ mutually exclusive? c. Find $B^c$ and $P\left(B^{\circ}\right)$.
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