Question #351003

3. QUESTION:

A bag contains ﬁfteen balls distinguishable only by their colours; ten are blue and ﬁve are red. I reach into the bag with both hands and pull out two balls (one with each hand) and record 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.

Expert's answer

1) The random phenomenon is colours of the two balls, which i have in my right and left hands.

2) The sample space is the set of all possible colours for the two balls in my hands.

If we define B - blue ball, R - red ball, then sample space is {(B, B),(B, R),(R, B),(R, R)}, when pairs (X, Y) show colors of balls in each our hand (X is colour in the left hand, Y is colour in the right hand).

3) The event "the ball in my left hand is red" is the subset {(R, B),(R, R)} because the ball in my right hand can be either red, or blue.

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