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An urn U1 contains 5 black balls and 4 white balls.

An urn U2 contains 4 black balls and 5 white balls

Part A.

We draw simultaneously 3 balls from U1.

1) Calculate the probability to get three balls of the same color.

2)Calculate the probability to get at least one black ball.

Part B.

We choose randomly one of the two urns and we draw Simultaneously two balls from the chosen urn.

Consider the following events :

E:The chosen urn is U1

F:The drawn balls are white.

1) Calculate P(F/E) and P(F).

2)The two drawn balls are white, calculate the probability that they come from U1?

My achievments so far : :

Part A.

!)P(3 balls of the same color from U1) = 5C3/9C3 + 4C3/9C3

2)Pr(at least 1 black) = all - non = 1 - 5C3/9C3

For Part B)

1)Pr(F/E) = 4C2/9C2

Pr(F) = 4C2/9C2 + 5C2/9C2.

2) P = P(F)/2.

I'm in too much need for help , I enjoy doing probability problems but I usually get them wrong !!

Notes : What's the difference between Simultaneously and successivly.

Many Thanks.

Aladdin