Two persons each make a single throw with a d | vedclass

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

Question

(C) For $p_1$: Two persons throw a die. Total outcomes = $6^2 = 36$. Favorable outcomes (both same) are $(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)$,so

Vedclass · Accepted Answer

$p_1 > p_2$

Vedclass · Answer

(C) For $p_1$: Two persons throw a die. Total outcomes = $6^2 = 36$. Favorable outcomes (both same) are $(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)$,so $6$ outcomes. Thus,$p_1 = \frac{6}{36} = \frac{1}{6} \approx 0.1667$.For $p_2$: Four persons throw a die. Total outcomes = $6^4 = 1296$. We want exactly three to be equal. First,choose the value that appears three times: $6$ ways. Choose the three persons who get this value: $\binom{4}{3} = 4$ ways. Choose the value for the fourth person (must be different from the first): $5$ ways. Total favorable outcomes = $6 	imes 4 	imes 5 = 120$.Thus,$p_2 = \frac{120}{1296} = \frac{5}{54} \approx 0.0926$.Comparing the two,$p_1 = \frac{9}{54}$ and $p_2 = \frac{5}{54}$,so $p_1 > p_2$.

Two persons each make a single throw with a die. The probability they get equal value is $p_1$. Four persons each make a single throw and the probability of exactly three being equal is $p_2$,then:

Similar Questions

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

Two numbers are selected at random from the first $40$ natural numbers. What is the probability that their sum is odd?

$A$ committee of $5$ is to be chosen from a group of $9$ people. The probability that a certain married couple will either serve together or not at all,is

If three distinct numbers are chosen randomly from the first $100$ natural numbers,then the probability that all three of them are divisible by both $2$ and $3$ is

The numbers $2, 3, 5, 7, 11, 13$ are written on six distinct paper chits. If $3$ of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by $3$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module