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 $A$ or $B$
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 $A$ or $B$
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,
$A =\left\{\begin{array}{l}(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(4,1),(4,2),(4,3) \\ (4,4),(4,5),(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
$B =\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(3,1),(3,2),(3,3) \\ (3,4),(3,5),(3,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\end{array}\right\}$
$C=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)\}$
$A$ or $B =A \cup B=\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6) \\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6) \\ (3,1),(3,2),(3,3),(3,4),(3,5),(3,6) \\ (4,1),(4,2),(4,3),(4,4),(4,5),(4,6) \\ (5,1),(5,2),(5,3),(5,4),(5,5),(5,6) \\ (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}=S$
Similar Questions
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$,
$B : 2$ occurs on either die
$C:$ the sum is at least $ 7$ and a multiple of $3.$
Which pairs of these events are mutually exclusive ?
An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the following events:
$A:$ the sum is greater than $8$,
$B : 2$ occurs on either die
$C:$ the sum is at least $ 7$ and a multiple of $3.$
Which pairs of these events are mutually exclusive ?
The probability of drawing a white ball from a bag containing $3$ black balls and $4$ white balls, is
The probability of drawing a white ball from a bag containing $3$ black balls and $4$ white balls, is
Three coins are tossed. Describe Two events which are mutually exclusive.
Three coins are tossed. Describe Two events which are mutually exclusive.
A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem is $\frac{1}{2} , \frac{1}{3} $ and $\frac{1}{4}$. Probability that the problem is solved is
A problem in Mathematics is given to three students $A, B, C$ and their respective probability of solving the problem is $\frac{1}{2} , \frac{1}{3} $ and $\frac{1}{4}$. Probability that the problem is solved is
- [AIEEE 2002]
$A$ and $B$ toss a coin alternatively, the first to show a head being the winner. If $A$ starts the game, the chance of his winning is
$A$ and $B$ toss a coin alternatively, the first to show a head being the winner. If $A$ starts the game, the chance of his winning is