Find the sample spaces for the following experiments and state the type of the s

Question

Find the sample spaces for the following experiments and state the type of the sample space, i.e. finite, uncountably infinite, countably infinite. (a) Two dice are thrown and the sum of the outcomes is measured. (b) Two balls are drawn from an urn containing six balls numbered 1 to 6, and the numbers are noted. (c) Pick a number X at random between 0 and 1, then pick a number Y at random between X and 1. (d) A coin is flipped until a head occurs. The number of times the coin is flipped before the first head appears is noted.

Explanation / Answer

Q.1 (a) Sample space : 2,3,4,5,6,7,8,9,10,11

Sample space here is finite.

(b) Sample space : (1,2), (1,3),(1,4),(1,5) ,(1,6), (2,3), (2,4),(2,5),(2,6), (3,4),(3,5),(3,6),(4,5),(4,6),(5,6)

the sample space is finite

(C) Sample space is { 0 < X < 1 ; X < Y< 1}

The sample space is uncountably infinite.

(D) Sample space : { k = 0,1,2,3,4,5.............infiinity}

The sample space is countably infinite.

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