2 dice are thrown. Find the probability of ge | vedclass

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

Question

(C) The total number of possible outcomes when throwing $2$ dice is $6 	imes 6 = 36$.Let $A$ be the event of getting an odd number on the first die a

Vedclass · Accepted Answer

$\frac{11}{36}$

Vedclass · Answer

(C) The total number of possible outcomes when throwing $2$ dice is $6 	imes 6 = 36$.Let $A$ be the event of getting an odd number on the first die and a multiple of $3$ on the second die.Odd numbers on a die are ${1, 3, 5}$. Multiples of $3$ on a die are ${3, 6}$.Possible outcomes for $(A, B)$ where $A \in {1, 3, 5}$ and $B \in {3, 6}$ are: $(1,3), (1,6), (3,3), (3,6), (5,3), (5,6)$. (Total $6$ outcomes).Let $C$ be the event of getting a multiple of $3$ on the first die and an odd number on the second die.Possible outcomes for $(C, D)$ where $C \in {3, 6}$ and $D \in {1, 3, 5}$ are: $(3,1), (3,3), (3,5), (6,1), (6,3), (6,5)$. (Total $6$ outcomes).The outcome $(3,3)$ is common to both sets.Using the inclusion-exclusion principle,the total number of unique favourable outcomes is $6 + 6 - 1 = 11$.The favourable outcomes are: $(1,3), (1,6), (3,3), (3,6), (5,3), (5,6), (3,1), (3,5), (6,1), (6,3), (6,5)$.Therefore,the required probability is $\frac{11}{36}$.

$2$ dice are thrown. Find the probability of getting an odd number on $1$ die and a multiple of $3$ on the other.

Similar Questions

The probability that an event will fail to happen is $0.05$. The probability that the event will take place on $4$ consecutive occasions is

In a simultaneous toss of $2$ coins,find the probability of getting no tail.

The probability that a leap year selected randomly will have $53$ Sundays is

In a single throw of two dice,the probability of obtaining an odd number as the sum is

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

Vedclass Test Series

Exam Paper Generator

Online Exam Module