Problem 2 (10 points). A box contains four white, two red, and one blue poker ch
ID: 3305543 • Letter: P
Question
Problem 2 (10 points). A box contains four white, two red, and one blue poker chips. Two chips are randomly chosen without replacement, and their colors noted. Each white chip has a value of 3 points each red chip has a value of 2 points and each blue chip has a value of 1 point each. Define the following events: A: (The two chips have a value of at least 5 points) whte B: (At least one of the chips is blue) C: (Both chips have different colors) Red = 2 Blu / a) Which (if any) of the above events are mutually exclusive? b) Compute P(AUB) and P(AUC). c) Compute P(CIB) and determine whether events B and C are independent.Explanation / Answer
a. If C occurs, the chips will have different colors and if the colors are white and red, the sum is 5 which also occurs in event A and if one of the chips is blue, this also happens in blue.
If B occurs, there will be one blue chip with 1 point and the sum will be a maximum of 1+3 = 4 and so A is not possible.
Thus A and B are mutually exclusive.
b. A can happen when neither chip is blue. B can happen when atleast one chip is blue. Since there is only blue chip, A and B cover all events
=> P(A U B) = 1.
A U C is the event that both chips have different colors or the sum is atleast five. Except for both red chips, the event is always true.
The two red chips can come in 4C2 = 6 ways.
Probability = 4C2/7C2 = 6/21 = 0.28.
c. C|B is the event that both chips have different colors given atleast one chip is blue. Since there is only one blue chip, this is always true.
P(C|B) = 1
But P(C) 1
=> P(C) P(C|B)
The two events are not independent.