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 $\leq 5$
Describe the events $A \cap B^{\prime} \cap C^{\prime}$
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 $\leq 5$
Describe the events $A \cap B^{\prime} \cap C^{\prime}$
When two dice are thrown, the sample space is given by
$s =\{(x, y): x, y=1,2,3,4,5,6\}$
$=\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right]$
Accordingly,
$A =\left\{\begin{array}{l}(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(4,1),(4,2),(4,3) \\ (4,4),(4,5),(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
$B =\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(3,1),(3,2),(3,3) \\ (3,4),(3,5),(3,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\end{array}\right\}$
$C=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)\}$
$C^{\prime}=\left\{\begin{array}{l}(1,5),(1,6),(2,4),(2,5),(2,6),(3,3),(3,4),(3,5),(3,6), \\ (4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),\\ (5,5),(5,6) ,(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
$A \cap B^{\prime} \cap C^{\prime}=A \cap A \cap C^{\prime}=A \cap C^{\prime}$
$=\left\{\begin{array}{l}(2,4),(2,5),(2,6),(4,2),(4,3),(4,4),(4,5) \\ (4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
Similar Questions
A card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.
A card is selected from a pack of $52$ cards. Calculate the probability that the card is an ace of spades.
If a coin be tossed $n$ times then probability that the head comes odd times is
If a coin be tossed $n$ times then probability that the head comes odd times is
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 knowing whether it is a boy or girl in the order of their births ?
For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.
The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is
For three non impossible events $A$, $B$ and $C$ $P\left( {A \cap B \cap C} \right) = 0,P\left( {A \cup B \cup C} \right) = \frac{3}{4},$ $P\left( {A \cap B} \right) = \frac{1}{3}$ and $P\left( C \right) = \frac{1}{6}$.
The probability, exactly one of $A$ or $B$ occurs but $C$ doesn't occur is
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is
A determinant is chosen at random from the set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen is non-zero is