A sample space consists of 9 elementary events E1,E2E3,....,E8,E9 whos

1.	A sample space consists of 9 elementary events E1,E2E3,....,E8,E9 whose probabilities are P(E1)=P(E2)=0.08, P(E3)=P(E4)=0.1, P(E6)=P(E7)=0.2 P(E8)=P(E9)=0.07 Suppose A={E1,E5,E8}, B ={E2,E5,E8,E9} (i) Compute P(A),P(B), P(A∩B) (ii) Using the addition law of probability, find P(A∪B) (iii) List the composition of the even A∪B, and calculate P(A∪B) by adding the probabilities of the elementary events. (iv) Calculate P(¯¯¯¯B) from P(B), also calculate P(¯¯¯¯B) directly from the elementary events of ¯¯¯¯B
Answer» A sample space consists of 9 elementary events $E_{1}, E_{2} E_{3}, . . . ., E_{8}, E_{9}$ whose probabilities are $P (E_{1}) = P (E_{2}) = 0.08,$ $P (E_{3}) = P (E_{4}) = 0.1,$ $P (E_{6}) = P (E_{7}) = 0.2$ $P (E_{8}) = P (E_{9}) = 0.07$ Suppose $A = {E_{1}, E_{5}, E_{8}}$ , B = ${E_{2}, E_{5}, E_{8}, E_{9}}$ (i) Compute $P (A), P (B)$ , $P (A \cap B)$ (ii) Using the addition law of probability, find $P (A \cup B)$ (iii) List the composition of the even $A \cup B$ , and calculate $P (A \cup B)$ by adding the probabilities of the elementary events. (iv) Calculate $P (¯ ¯¯ ¯ B)$ from $P (B)$ , also calculate $P (¯ ¯¯ ¯ B)$ directly from the elementary events of $¯ ¯¯ ¯ B$

A sample space consists of 9 elementary events E1,E2E3,....,E8,E9 whose probabilities are P(E1)=P(E2)=0.08, P(E3)=P(E4)=0.1, P(E6)=P(E7)=0.2 P(E8)=P(E9)=0.07 Suppose A={E1,E5,E8}, B ={E2,E5,E8,E9} (i) Compute P(A),P(B), P(A∩B) (ii) Using the addition law of probability, find P(A∪B) (iii) List the composition of the even A∪B, and calculate P(A∪B) by adding the probabilities of the elementary events. (iv) Calculate P(¯¯¯¯B) from P(B), also calculate P(¯¯¯¯B) directly from the elementary events of ¯¯¯¯B

Answer»

A sample space consists of 9 elementary events

$E_{1}, E_{2} E_{3}, . . . ., E_{8}, E_{9}$

whose probabilities are

$P (E_{1}) = P (E_{2}) = 0.08,$

$P (E_{3}) = P (E_{4}) = 0.1,$

$P (E_{6}) = P (E_{7}) = 0.2$

$P (E_{8}) = P (E_{9}) = 0.07$

Suppose $A = {E_{1}, E_{5}, E_{8}}$ ,

B = ${E_{2}, E_{5}, E_{8}, E_{9}}$

(i) Compute $P (A), P (B)$ , $P (A \cap B)$

(ii) Using the addition law of probability, find $P (A \cup B)$

(iii) List the composition of the even $A \cup B$ , and calculate

$P (A \cup B)$ by adding the probabilities of the elementary events.

(iv) Calculate $P (¯ ¯¯ ¯ B)$ from $P (B)$ , also calculate

$P (¯ ¯¯ ¯ B)$ directly from the elementary events of $¯ ¯¯ ¯ B$