A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $3$.
A fair coin with $1$ marked on one face and $6$ on the other and a fair die are both tossed. find the probability that the sum of numbers that turn up is $3$.
since the fair coin has $1$ marked on one face and $6$ on the other, and the die has six faces that are numbered $1,\,2,\,3\,,4,\,5,$ and $6,$ the sample space is given by
$S =\{(1,1),(1,2),(1,3),(1,4)$, $(1,5),(1,6),(6,1)$, $(6,2),(6,3),(6,4),(6,5),(6,6)\}$
Accordingly, $n ( S )=12$
Let $A$ be the event in which the sum of numbers that turn up is $3$.
Accordingly, $A=\{(1,2)\}$
$\therefore P(A)=\frac{\text { Number of outcomes favourable to } A}{\text { Total number of possible outcomes }}=\frac{n(A)}{n(S)}=\frac{1}{12}$
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Let $\mathrm{X}$ and $\mathrm{Y}$ be two events such that $\mathrm{P}(\mathrm{X})=\frac{1}{3}, \mathrm{P}(\mathrm{X} \mid \mathrm{Y})=\frac{1}{2}$ and $\mathrm{P}(\mathrm{Y} \mid \mathrm{X})=\frac{2}{5}$. Then
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- [IIT 2017]
Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to
Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to
- [JEE MAIN 2023]
Two dice are thrown. The events $A,\, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
State true or false $:$ (give reason for your answer)
Statement : $A$ and $B^{\prime }$ are mutually exclusive
Two dice are thrown. The events $A,\, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$
State true or false $:$ (give reason for your answer)
Statement : $A$ and $B^{\prime }$ are mutually exclusive