Two dice are thrown simultaneously. The proba | vedclass

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

Question

(C) Let $A$ be the event that the sum is less than $7$ and $B$ be the event that the sum is odd.Total outcomes when two dice are thrown $= 6 	imes 6

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(C) Let $A$ be the event that the sum is less than $7$ and $B$ be the event that the sum is odd.Total outcomes when two dice are thrown $= 6 	imes 6 = 36$.Outcomes for $A$ (sum $$P(A) = \frac{15}{36}$.Outcomes for $B$ (sum is odd): Sums can be $3, 5, 7, 9, 11$. Total $= 18$.$P(B) = \frac{18}{36}$.Outcomes for $A \cap B$ (sum is odd $AND$ less than $7$): Sums can be $3, 5$. Outcomes are $(1,2), (2,1), (1,4), (2,3), (3,2), (4,1)$. Total $= 6$.$P(A \cap B) = \frac{6}{36}$.Using the addition theorem: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.$P(A \cup B) = \frac{15}{36} + \frac{18}{36} - \frac{6}{36} = \frac{27}{36} = \frac{3}{4}$.

Two dice are thrown simultaneously. The probability that the sum is odd or less than $7$ or both is:

Similar Questions

Let $A, B,$ and $C$ be events such that $P(A) = P(B) = P(C) = \frac{1}{4}, P(AB) = P(CB) = 0,$ and $P(AC) = \frac{1}{8}.$ Then $P(A \cup B) = \dots$

If a card is drawn at random from a well-shuffled pack of $52$ playing cards,then the probability that it is either an ace or a spade card is

The probabilities of occurrence of two events are respectively $0.21$ and $0.49$. The probability that both occur simultaneously is $0.16$. Then the probability that none of the two occurs is

The odds in favour of getting a sum that is a multiple of $3$,when a pair of dice is thrown,is:

$A$ speaks the truth in $75\%$ of cases and $B$ speaks the truth in $80\%$ of cases. What is the probability that they contradict each other in stating the same fact?

Vedclass Test Series

Exam Paper Generator

Online Exam Module