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21. Two fair coins are tossed. Let E be the event not more than one h.pdf

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21. Two fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HH, HT, TH, TT) and assign probability ¼ to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? 23. Three fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HHH, HHT, ..., TTT} and assign probability 1/8 to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? Solution 21. a) E be the Event = { Not more than one Head } = {(H,T) (T,H) (T,T) } b) F be the Event = { atleast one of each face } = { (H,T) (T,H)} = Sample Space = { (H,T) (T,H) (T,T) (H,H) } c. P( E n F) = {(H,T) (T,H)} d. Dependent Note : We are suppose to answer only 1 question in time.

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21. Two fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HH, HT, TH, TT) and assign probability ¼ to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? 23. Three fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HHH, HHT, ..., TTT} and assign probability 1/8 to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? Solution 21. a) E be the Event = { Not more than one Head } = {(H,T) (T,H) (T,T) } b) F be the Event = { atleast one of each face } = { (H,T) (T,H)} = Sample Space = { (H,T) (T,H) (T,T) (H,H) } c. P( E n F) = {(H,T) (T,H)} d. Dependent Note : We are suppose to answer only 1 question in time

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  • 1. 21. Two fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HH, HT, TH, TT) and assign probability ¼ to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? 23. Three fair coins are tossed. Let E be the event not more than one head and F the event at least one of each face. Define the sample space S = {HHH, HHT, ..., TTT} and assign probability 1/8 to each simple event. a. Determine the P(E) b. Find the P(F) c. Find the P(E intersection F) d. Are E and F independent or dependent? Solution 21. a) E be the Event = { Not more than one Head } = {(H,T) (T,H) (T,T) } b) F be the Event = { atleast one of each face } = { (H,T) (T,H)} = Sample Space = { (H,T) (T,H) (T,T) (H,H) } c. P( E n F) = {(H,T) (T,H)} d. Dependent Note : We are suppose to answer only 1 question in time