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2 answers:
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Answer:
a) No, because the probabilities of winning the 2nd game are dependant on the result of the 1st game. The probabilities are different if you win or lose the first game.
b) P=0.42
c) P=0.08
d)
X | P(X)
------------------
0 | 0.42
1 | 0.50
2 | 0.08
e) E(x)=0.66
s.d.=0.62
Step-by-step explanation:
a) No, because the probabilities of winning the 2nd game are dependant on the result of the 1st game. The probabilities are different if you win or lose the first game.
b) The probability of losing the first game is
The probability of losing the second game, given that the first game was lost is:
So the probability of losing both games is:
c) The probability of winning both games is:
d) The variable X can take values 0, 1 and 2.
X=0 is when both games are lost. This happens with probability P=0.42.
X=2 is when both games are won. This happens with probability P=0.08.
X=1 is when one game is won and the other is lost. This happens with probability P=1-0.42-0.08=0.50.
Then the table of probabilities become:
X | P(X)
------------------
0 | 0.42
1 | 0.50
2 | 0.08
e) The expected value is:
The variance and standard deviation of x are:
The standard deviation can