$A$ 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 a head,we throw a die. Find the sample space for this experiment.
The box contains $2$ red balls and $3$ black balls. Let us denote the $2$ red balls as $R_{1}, R_{2}$ and the $3$ black balls as $B_{1}, B_{2}, B_{3}$.
The sample space $S$ of this experiment is the set of all possible outcomes.
If the coin shows a tail $(T)$,we draw a ball from the box,resulting in outcomes: $TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}$.
If the coin shows a head $(H)$,we throw a die,resulting in outcomes: $H1, H2, H3, H4, H5, H6$.
Therefore,the sample space is $S = \{TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}, H1, H2, H3, H4, H5, H6\}$.
The sample space $S$ of this experiment is the set of all possible outcomes.
If the coin shows a tail $(T)$,we draw a ball from the box,resulting in outcomes: $TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}$.
If the coin shows a head $(H)$,we throw a die,resulting in outcomes: $H1, H2, H3, H4, H5, H6$.
Therefore,the sample space is $S = \{TR_{1}, TR_{2}, TB_{1}, TB_{2}, TB_{3}, H1, H2, H3, H4, H5, H6\}$.
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Similar Questions
Let $A$ and $B$ be events in a sample space $S$ such that $P(A)=0.5, P(B)=0.4$ and $P(A \cup B)=0.6$. Observe the following lists. The correct match of List $I$ from List $II$ is:
List $I$ List $II$ $(i) \ P(A \cap B)$ $(1) \ 0.4$ $(ii) \ P(A \cap \bar{B})$ $(2) \ 0.2$ $(iii) \ P(\bar{A} \cap B)$ $(3) \ 0.3$ $(iv) \ P(\bar{A} \cap \bar{B})$ $(4) \ 0.1$
| List $I$ | List $II$ |
| $(i) \ P(A \cap B)$ | $(1) \ 0.4$ |
| $(ii) \ P(A \cap \bar{B})$ | $(2) \ 0.2$ |
| $(iii) \ P(\bar{A} \cap B)$ | $(3) \ 0.3$ |
| $(iv) \ P(\bar{A} \cap \bar{B})$ | $(4) \ 0.1$ |
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