Provide a representation of the sample space for each of the following experimen

Question

Provide a representation of the sample space for each of the following experiments.

(a) Two balls are selected at random with replacement from a box containing 5 red balls and 15 green balls and the colors of the two balls are recorded.

(b) Redo part (a) assuming that only the number of red balls in the selection is recorded.

(c) Two balls are selected at random without replacement from a box containing 5 red balls and 15 green balls and the colors of the two balls are recorded.

(d) Redo part (c) assuming that only the number of red balls in the selection is recorded.

(e) A balanced die is tossed once the number on the die is noted, call it n, and then a coin is tossed n times and the number of heads in the n tosses is recorded.

Explanation / Answer

a) Here as there are a total of 2 colours possible and 2 balls are drawn. Therefore the sample space for the given experiment would be given as:

S = { RR, RG, GR, GG }

b) Here we are recording the number of red balls drawn out of the 2 balls drawn. As the total number of balls drawn are 2, therefore there could only be either 0,1 or 2 red balls drawn. Therefore the sample space here would be given as:

S = { 0, 1, 2 }

c) Even when the balls are drawn without replacement. Still there is a possiblility of either having both red balls, one red ball or 0 red balls. Therefore the sample spaces for the 2 above parts would remain the same as:

S1 = { RR, RG, GR, GG } and

d) S2 = { 0, 1, 2 }

e) Here we are recording the number of coin tosses that had heads. Now the value of n can obviously range from 1 to 6. Therefore there could be max 6 heads and minimum 0 heads ( in case all are tails ) . Therefore the sample space here would be obtained as:

S = { 0, 1, 2, 3, 4, 5, 6 }

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