Two players,P_1 and P_2,play a game against e | vedclass

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

Question

(A) Let $W$ be the event $P_1$ wins a round,$L$ be $P_1$ loses,and $D$ be a draw.$P(D) = \frac{6}{36} = \frac{1}{6}$.$P(W) = P(L) = \frac{1}{2}(1 - \f

Vedclass · Accepted Answer

$(I) \rightarrow (Q); (II) \rightarrow (R); (III) \rightarrow (T); (IV) \rightarrow (S)$

Vedclass · Answer

(A) Let $W$ be the event $P_1$ wins a round,$L$ be $P_1$ loses,and $D$ be a draw.$P(D) = \frac{6}{36} = \frac{1}{6}$.$P(W) = P(L) = \frac{1}{2}(1 - \frac{1}{6}) = \frac{5}{12}$.For $n=2$:$P(X_2 > Y_2) = P(W, W) + P(W, D) + P(D, W) = (\frac{5}{12})^2 + 2(\frac{5}{12} 	imes \frac{1}{6}) = \frac{25}{144} + \frac{20}{144} = \frac{45}{144} = \frac{5}{16}$. (Matches $II ightarrow R$)$P(X_2 = Y_2) = P(D, D) + P(W, L) + P(L, W) = (\frac{1}{6})^2 + 2(\frac{5}{12} 	imes \frac{5}{12}) = \frac{1}{36} + \frac{50}{144} = \frac{4+50}{144} = \frac{54}{144} = \frac{3}{8}$. (Matches $I ightarrow P$)$P(X_2 \geq Y_2) = P(X_2 > Y_2) + P(X_2 = Y_2) = \frac{5}{16} + \frac{3}{8} = \frac{11}{16}$. (Matches $I ightarrow Q$ is incorrect,$I ightarrow P$ is correct for $X_2=Y_2$)Wait,$P(X_2 \geq Y_2) = \frac{11}{16}$ matches $Q$. So $I ightarrow Q$.For $n=3$:$P(X_3 = Y_3) = P(D, D, D) + 3P(W, L, D) + 3P(W, W, L, L) \dots$ calculation yields $\frac{77}{432}$. (Matches $III ightarrow T$)$P(X_3 > Y_3) = \frac{1}{2}(1 - P(X_3 = Y_3)) = \frac{1}{2}(1 - \frac{77}{432}) = \frac{355}{864}$. (Matches $IV ightarrow S$)Thus,$I ightarrow Q, II ightarrow R, III ightarrow T, IV ightarrow S$.

List-$I$	List-$II$
$(I)$ Probability of $(X_2 \geq Y_2)$ is	$(P)$ $\frac{3}{8}$
$(II)$ Probability of $(X_2 > Y_2)$ is	$(Q)$ $\frac{11}{16}$
$(III)$ Probability of $(X_3 = Y_3)$ is	$(R)$ $\frac{5}{16}$
$(IV)$ Probability of $(X_3 > Y_3)$ is	$(S)$ $\frac{355}{864}$
	$(T)$ $\frac{77}{432}$

Similar Questions

Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If $A$ is the event of getting a sum greater than $14$ and $B$ is the event of getting a sum which is a multiple of $3$,then $P(A \cap \overline{B}) + P(\overline{A} \cap B) = $

Two events $A$ and $B$ will be independent,if

The corners of regular tetrahedrons are numbered $1, 2, 3, 4$. Three tetrahedrons are tossed. The probability that the sum of the upward corners will be $5$ is

If $n$ numbers are chosen at random from the set $\{1, 2, 3, \dots, 1000\}$,what is the probability that $\frac{\sum_{i=1}^n i^2}{\sum_{i=1}^n i}$ is an integer?

If two smallest squares are chosen at random on a chessboard, then the probability of choosing these squares such that they do not have a side in common is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module