A coin is tossed. If the outcome 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?

Solution

A coin is tossed. The sample space,
$straight S subscript 1 space equals space left curly bracket straight H comma space straight T right curly bracket$
For T, there is no further action.
For H, a die is rolled with sample space
$straight S subscript 2 equals left curly bracket 1 comma space 2 comma space 3 comma space 4 comma space 5 space 6 right curly bracket$
For H1, H3, H5, no further action.
For H2, H4, H6, die is rolled again
∴ The combined space is
S = {T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66}

Some More Questions From Straight Lines Chapter

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

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Straight Lines

A coin is tossed. If the outcome 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?

Some More Questions From Straight Lines Chapter

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?

An experiment consists of recording boy-girl composition of families with 2 children. What is the sample space if we are interested in the number of girls in the family?

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

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