Conditional Probability Worksheet Page 3

23. All the diamonds are removed from a standard pack of cards, and a card is taken at

random from this reduced pack. If K is the event the card is a King, and S is the event

the card is a Spade, are K and S independent?

Yes, P (S) × P (K) = P (S ∩ K) =

24. If A is independent of B, (i.e. the occurrence of B doesn’t change the probability of A

happening), does it also imply that B is independent of A? Prove it!

Yes

25. The random events A,B and C are deﬁned in a ﬁnite sample space S. A and B are

mutually exclusive and A and C are independent. P(A) =

, P(B) =

, P(A ∪ C) =

and P(B ∪ C) =

. Evaluate P(A ∪ B), P(A ∩ B), P(A ∩ C), and P(B ∩ C), and state

whether B and C are independent.

, 0,

, no

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