From the given table, we can deduce the following:
P(win) = 0.9
P(loss) = 0.1
P(Playing at home) = 0.7
P(Playing away) = 0.3
P(win at home) = 0.63
P(win away) = 0.27
P(Loss away) = 0.03
P(loss home) = 0.07
• (a) Are the events winning and playing at home independent.
Independent events are events that do not affect the probability of each other occuring.
We have:
P(winning) = 0.9
P(playing at home) = 0.7
P(win and playing at home) = 0.63
To determine if the events winning and playing at home is independent, we have:
P(win and playing at home) = P(win) x P(playing at home) = 0.9 x 0.7 = 0.63
0.63 = 0.9 x 0.7
0.63 = 0.63
Since the equation is true, the events winning and playing at home are independent.
• (b) Are the events "losing" and "playing away" independent? Show your calculations to justify why or why not.
From the table, we hae:
P(losing) = 0.1
P(Playing away) = 0.3
P(Losing and playing away) = 0.03
To determine if the events are independent or not, we have:
P(losing and playing away) = P(losing) x P(playing away)
0.03 = 0.1 x 0.3
0.03 = 0.03
SInce the equation is true, both events are independent.
ANSWER:
(a) The events are indepedent
(b) The events are indepedent