question 1:
the casino has tow types of gambling machine , type A and type B , the winning probability of type A is 20%,and the winning probability of type B is 30%, so if we know that 60% of gambling machine in casino are type A , and 40% are type B :
(a) one gambler select randomly one gampling machine and played , what is the probability that he will win ?
(b)if the gambler win, what is the probability that the machine gambling from type B?
Let us define the given events first.
W - the gambler wins
A - the gambler plays on type A gambling machine
B - the gambler plays on type B gambling machine
We will use c as subscript to represent complementary events.
Now let us find the mathemetical representation of the given statements of probabilities.
The winning probability of type A is 20%
The winning probability of type B is 30%
60% of the gambling machine in casino are type A.
40% machines are type B
(a)
For this part we have to find the probability of winning. This will be given by,
(b)
The required probability would be given by,
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