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1. Roll a pair of dice, one red and one green. Now, define the following events: A is the event that at least one of the dice will be an even number B is the event that the sum of the die will be equal to 7; C is the event that at least one of the dice is equal to 1 (a) Draw a picture of the sample space. (b) List all the outcomes for each of the events A, B and C explicitly. (c) Highlight/label each of the events on your picture of the sample space. (If you feel it is necessary, you may draw a new picture for each event.) d) Find P(A), P(B), and P(C) (e) Are events A and C independent? Explain using appropriate probabilities and/or theo- (f) Are events B and C disjoint (mutually exclusive)? Explain using appropriate probabilities (g) What is the relationship between P(A) and P(B)? Fill in the blank with one of the following rems? and/or theorems? symbols: s,2P(A) P(B) Explain using appropriate theorems and/or definitions why this makes sense.

math   Statistics-And-Probability   
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Page-1 a) Somple space (4,1у (4,2) (4,3) (4,4) (4,5) l4ς) A={(1,2) (1,49 (LE) (2,1) (2,21 («, 3) (2,4) (2,5) (2.c) (3,2) 4,3I. 3 C e Are the ents A andc indapendent T wo events A andc defined sample space 1- ar saidl to be indepen- on a dent if ond onl f ncAnc): С 3 SPaae-3 12. 2 A ond c ar* not ndependert Are events B and c disjont ? B and c an said o be dusjoint Bond c ан.rat d isjeïnt.

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