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 $B$ and $C$
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 $B$ and $C$
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,
$A =\left\{\begin{array}{l}(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(4,1),(4,2),(4,3) \\ (4,4),(4,5),(4,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\end{array}\right\}$
$B =\left\{\begin{array}{l}(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(3,1),(3,2),(3,3) \\ (3,4),(3,5),(3,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)\end{array}\right\}$
$C=\{(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(3,1),(3,2),(4,1)\}$
$B$ and $C = B \cap C \quad\{(1,1),(1,2),(1,3),(1,4),(3,1),(3,2)\}$
Similar Questions
If any four numbers are selected and they are multiplied, then the probability that the last digit will be $1, 3, 5$ or $7$ is
If any four numbers are selected and they are multiplied, then the probability that the last digit will be $1, 3, 5$ or $7$ is
The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is
The probability of happening an event $A$ in one trial is $0.4$. The probability that the event $A$ happens at least once in three independent trials is
- [IIT 1980]
If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $
If $A$ and $B$ are two independent events such that $P\,(A \cap B') = \frac{3}{{25}}$ and $P\,(A' \cap B) = \frac{8}{{25}},$ then $P(A) = $
- [IIT 2002]
A single letter is selected at random from the word “$PROBABILITY$”. The probability that the selected letter is a vowel is
A single letter is selected at random from the word “$PROBABILITY$”. The probability that the selected letter is a vowel is
Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.
Describe the sample space for the indicated experiment: A coin is tossed and then a die is rolled only in case a head is shown on the coin.