Suppose you are given one blue urn and three green urns, in a dark room so that you cannot tell the difference between the urns. The blue urn contains seven red balls and three yellow balls. Each green urn contains three red balls and seven yellow balls. You draw a ball at random from one of the urns.

Let event A

1

1

be drawing a ball from a blue urn. What is the probability of event A

1

1

expressed as a fraction? P(A

1

1

) =/

Let event A

2

2

be drawing a ball from a green urn. What is the probability of event A

2

2

expressed as a fraction? P(A

2

2

) =/

Let event B be drawing a red ball. Assuming the urn is blue, what is the probability of drawing a red ball from the blue urn, expressed as a fraction? P(B given A

1

1

) =/

Let event B be drawing a red ball. Assuming the urn is green, what is the probability of drawing a red ball from the green urn, expressed as a fraction? P(B given A

2

2

) =/

Assuming you draw a red ball from one of the urns, what is the (decimal) probability that the urn was blue according to Bayes's Theorem? P(A

1

1

given B) =