Two balanced dice are rolled. Find the probab | vedclass

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(B) When two balanced dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$.We need to find the probability that the sum of the n

Vedclass · Accepted Answer

$\frac{5}{12}$

Vedclass · Answer

(B) When two balanced dice are rolled,the total number of possible outcomes is $6 	imes 6 = 36$.We need to find the probability that the sum of the numbers on the two dice is less than $7$.The possible outcomes where the sum is less than $7$ are:Sum $= 2$: $(1, 1)$ ($1$ outcome)Sum $= 3$: $(1, 2), (2, 1)$ ($2$ outcomes)Sum $= 4$: $(1, 3), (2, 2), (3, 1)$ ($3$ outcomes)Sum $= 5$: $(1, 4), (2, 3), (3, 2), (4, 1)$ ($4$ outcomes)Sum $= 6$: $(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)$ ($5$ outcomes)Total favorable outcomes $= 1 + 2 + 3 + 4 + 5 = 15$.The probability is given by $\frac{	ext{Number of favorable outcomes}}{	ext{Total number of outcomes}} = \frac{15}{36}$.Simplifying the fraction by dividing both numerator and denominator by $3$,we get $\frac{15 \div 3}{36 \div 3} = \frac{5}{12}$.

Two balanced dice are rolled. Find the probability that the sum of numbers on two dice is smaller than $7$.

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