Find the probability if more than one M&M; is chosen with replacement a) p(red a

Question

Find the probability if more than one M&M; is chosen with replacement a) p(red and yellow) = ____ b) p(green and green and green) = ___ c) p(brown and red) = ______ d)p(red and green and orange) = ________ Find the following complement probabilities: a)p(not red) = _______ b) p(complement of blue) = _________ A. If two or more M&M;'s are chosen without replacement, are the events independent? Why or why not? B. If two or more M&M;'s are chosen with replacement, are the events independent? Why or why not? Are the M&M;'s mutually exclusive

Explanation / Answer

P( red and yellow ) = P(red) * P(yellow)= 0.138 * 0.174 = 0.024012

P ( green and green and green) = [ P(green) ]3 = (0.211) ^3 = 0.00939

P(brown and red) = P(brown) *P(red) = 0.128*0.138 = 0.017664

P(red and green and orange) = P(red) *P(green)*P(orange) = 0.138* 0.211* 0.156 =0.00454

2. P(not red) = 1- P(red) = 1- 0.138 = 0.862

P( complement of blue) = P(not blue) = 1-P(blue)= 1- 0.193 = 0.807

3. When 2 M&Ms are selected Without Replacement the events are not independent, because the outcome of the first selection affects the 2 selection, eg if a red is picked in the first draw then the probabilty of the 2 nd draw not being a red would be higher (1 ) , than it was in the first draw (0.862) , as we know the first draw resulted in red M&M.

3. with replacement maintains independence of the draws, the oucome of the first draw doesnot affect the outcome of the second draw.

4. Yes the M&M's are mutually exculsive as there is no intersection among events of the M&Ms being different colours.

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