Question

1. USC and UCLA decide to host a group Halloween carnival. Students are encouraged to come in costume, but only some of them do. The following chart summarizes this information:

	Costume	No Costume	Total
UCLA	311	129	440
USC	250	150	400
Total	561	279	840

1. Are the events “wears a costume” and “attends UCLA” independent? Why or why not?

Answer 1

P(Wears a costume) = 561 / 840

P(attends UCLA ) = 440 / 840

Two events A and B are independent if P(A and B) = P(A) * P(B)

P(wears a costume AND attends UCLA) = 311 / 840

Now

P(Wears a costume) * P(attends UCLA ) = 561/840 * 440 / 840 = 2057 / 5880

Since

P(wears a costume AND attends UCLA) P(Wears a costume) * P(attends UCLA )

The events “wears a costume” and “attends UCLA” are not independent