Two dice are thrown together and the total score is noted. The event E, F and G are “a total 4”, “a total of 9 or more”, and “a total divisible by 5”, respectively. Calculate P(E), P(F) and P(G) and decide which pairs of events, if any, are independent.

Question

Philoid · Accepted Answer

We are throwing two dice so,

Sample space S={(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),

(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),

(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),

(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),

(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),

(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Sample space contains 36 elements,

n(S)=36

let E be an event of getting sum 4

E={(1,3),(3,1),(2,2)}

n(E)=3

F be the event of getting 9 or more

F ={(3,6),(6,3),(4,5),(5,4),(4,6),(6,4),(5,5),(5,6),(6,5),(6,6)}

n(F)=3

G be the event getting a total divisible by 5

G= {(1,4),(4,1),(2,3),(3,2),(4,6),(6,4),(5,5)}

n(G)=7

So E and F are not independent

So E and G are not independent

So F and G are not independent

Therefore no pair is independent