In a single throw of 2 dice,what is the proba | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) When $2$ dice are thrown,the total number of possible outcomes is $6 	imes 6 = 36$.Let $A$ be the event of getting a multiple of $2$ on the first

Vedclass · Accepted Answer

$\frac{11}{36}$

Vedclass · Answer

(C) When $2$ dice are thrown,the total number of possible outcomes is $6 	imes 6 = 36$.Let $A$ be the event of getting a multiple of $2$ on the first die: $A = \{2, 4, 6\}$.Let $B$ be the event of getting a multiple of $3$ on the second die: $B = \{3, 6\}$.We need to find the probability of getting a multiple of $2$ on one die and a multiple of $3$ on the other.Let $E_1$ be the set of outcomes where the first die is a multiple of $2$ and the second is a multiple of $3$: $E_1 = \{(2,3), (2,6), (4,3), (4,6), (6,3), (6,6)\}$.Let $E_2$ be the set of outcomes where the first die is a multiple of $3$ and the second is a multiple of $2$: $E_2 = \{(3,2), (3,4), (3,6), (6,2), (6,4), (6,6)\}$.The union $E_1 \cup E_2$ represents the favourable outcomes. Note that $(6,6)$ is common to both sets.$E_1 \cup E_2 = \{(2,3), (2,6), (4,3), (4,6), (6,3), (6,6), (3,2), (3,4), (6,2), (6,4)\}$.Counting the unique elements,the number of favourable outcomes is $11$.Therefore,the required probability is $\frac{11}{36}$.

In a single throw of $2$ dice,what is the probability of getting a multiple of $2$ on one die and a multiple of $3$ on the other?

Similar Questions

There are $n$ different objects $1, 2, 3, \dots, n$ distributed at random in $n$ places marked $1, 2, 3, \dots, n$. The probability that at least three of the objects occupy places corresponding to their number is

When $2$ dice are thrown,find the probability of getting a sum that is a prime number.

An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events,then the probability of happening neither $A$ nor $B$ is

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a card of spade. The probability that he will fail the first two times is

Vedclass Test Series

Exam Paper Generator

Online Exam Module