A bag contains fifteen balls distinguishable only by their colours; ten are blue and five arered. I reach into the bag with both hands and pull out two balls (one with each hand) andrecord their colours.(a) What is the random phenomenon?(b) What is the sample space?(c) Express the event that the ball in my left hand is red as a subset of the sample space.
Question
A bag contains fifteen balls distinguishable only by their colours; ten are blue and five arered. I reach into the bag with both hands and pull out two balls (one with each hand) andrecord their colours.(a) What is the random phenomenon?(b) What is the sample space?(c) Express the event that the ball in my left hand is red as a subset of the sample space.
Solution
(a) The random phenomenon in this scenario is the act of reaching into the bag and pulling out two balls, with their colors being the outcome of interest.
(b) The sample space, which is the set of all possible outcomes, would be: {(Blue, Blue), (Blue, Red), (Red, Blue), (Red, Red)}. This represents all the possible combinations of colors that can be pulled out from the bag with two hands.
(c) The event that the ball in the left hand is red can be expressed as a subset of the sample space as follows: {(Red, Blue), (Red, Red)}. This subset includes all outcomes where a red ball ends up in the left hand.
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