A coin is tossed. If the out come is a head a die is thrown. If the die shows up an even number the die is thrown again. What is the sample space for the experiment?

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Solution

When a coin is tossed the possible outcomes are head $(H)$ and tail $(T)$
When a die is thrown the possible outcomes are $1, 2, 3, 4, 5$ or $6$
Thus the sample space of this experiment is given by :
$S = T, H_{1}, H_{3}, H_{5}, H_{21}, H_{22}, H_{23}, H_{24}, H_{25}, H_{26}, H_{41}, H_{42}, H_{43}, H_{44}, H_{45}, H_{46}, H_{61}, H_{62}, H_{63}, H_{64}, H_{65}, H_{66}$

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A coin is tossed. If the out come is a head a die is thrown. If the die shows up an even number the die is thrown again. What is the sample space for the experiment?

When a coin is tossed the possible outcomes are head (H) and tail (T)When a die is thrown the possible outcomes are 1,2,3,4,5 or 6Thus the sample space of this experiment is given by :S=T,H1,H3,H5,H21,H22,H23,H24,H25,H26,H41,H42,H43,H44,H45,H46,H61,H62,H63,H64,H65,H66