$A$ 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?
(N/A) 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 $6$.
If the coin shows $T$,the experiment ends.
If the coin shows $H$,a die is thrown. If the result is odd $(1, 3, 5)$,the experiment ends.
If the result is even $(2, 4, 6)$,the die is thrown again.
Thus,the sample space $S$ is:
$S = \{T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66\}$
When a die is thrown,the possible outcomes are $1, 2, 3, 4, 5,$ or $6$.
If the coin shows $T$,the experiment ends.
If the coin shows $H$,a die is thrown. If the result is odd $(1, 3, 5)$,the experiment ends.
If the result is even $(2, 4, 6)$,the die is thrown again.
Thus,the sample space $S$ is:
$S = \{T, H1, H3, H5, H21, H22, H23, H24, H25, H26, H41, H42, H43, H44, H45, H46, H61, H62, H63, H64, H65, H66\}$
Explore More
Similar Questions
Two students Anil and Ashima appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10$. The probability that both will qualify the examination is $0.02$. Find the probability that both Anil and Ashima will not qualify the examination.
Medium
View SolutionSuppose $3$ bulbs are selected at random from a lot. Each bulb is tested and classified as defective $(D)$ or non-defective $(N)$. Write the sample space of this experiment.
Easy
View SolutionThree coins are tossed. Describe three events which are mutually exclusive and exhaustive.
Medium
View SolutionTwo fair dice are rolled. The probability of the sum of digits on their faces being greater than or equal to $10$ is
Thirty-two persons $X_1, X_2, \ldots, X_{32}$ are randomly seated around a circular table at equal intervals. Two persons $X_i$ and $X_j$ are said to be within earshot of each other if there are at most three persons between them on the minor arc joining $X_i$ and $X_j$. The probability that $X_1$ and $X_3$ are within earshot of each other is:
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo