If A and B throw two dice 100 times each simu | vedclass

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(B) Let $S_A$ be the sum of the two dice thrown by $A$ and $S_B$ be the sum of the two dice thrown by $B$. For the sum of two dice to be even,both dic

Vedclass · Accepted Answer

$\left(\frac{1}{4}\right)^{100}$

Vedclass · Answer

(B) Let $S_A$ be the sum of the two dice thrown by $A$ and $S_B$ be the sum of the two dice thrown by $B$. For the sum of two dice to be even,both dice must show either both even numbers or both odd numbers. The probability of getting an even sum for one person is $P(	ext{even}) = \frac{18}{36} = \frac{1}{2}$. Since $A$ and $B$ throw simultaneously and independently,the probability that both get an even sum in a single trial is $P(A_{	ext{even}} \cap B_{	ext{even}}) = P(A_{	ext{even}}) 	imes P(B_{	ext{even}}) = \frac{1}{2} 	imes \frac{1}{2} = \frac{1}{4}$. Since they perform this experiment $100$ times,the probability that both get an even sum in all $100$ throws is $\left(\frac{1}{4}ight)^{100}$.

If $A$ and $B$ throw two dice $100$ times each simultaneously,then the probability that both of them will get an even number as the total score at the same time in all the throws is

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