Question

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?

Answer 1

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,