21 Two fair coins are tossed Let E be the event not more tha

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