In a game,a man wins ₹ 40 if he gets 5 or 6 o | vedclass

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

Question

(C) Let $S$ be the event of getting $5$ or $6$ (success) and $F$ be the event of getting $1, 2, 3,$ or $4$ (failure).Probability of success $P(S) = \f

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(C) Let $S$ be the event of getting $5$ or $6$ (success) and $F$ be the event of getting $1, 2, 3,$ or $4$ (failure).Probability of success $P(S) = \frac{2}{6} = \frac{1}{3}$.Probability of failure $P(F) = 1 - \frac{1}{3} = \frac{2}{3}$.The game stops if he gets $S$ or after $3$ throws.Possible outcomes:$1$. Success on 1st throw: $S$. Probability $P_1 = \frac{1}{3}$. Gain = $₹ 40$.$2$. Success on 2nd throw: $FS$. Probability $P_2 = \frac{2}{3} 	imes \frac{1}{3} = \frac{2}{9}$. Gain = $40 - 20 = ₹ 20$.$3$. Success on 3rd throw: $FFS$. Probability $P_3 = \frac{2}{3} 	imes \frac{2}{3} 	imes \frac{1}{3} = \frac{4}{27}$. Gain = $40 - 20 - 20 = ₹ 0$.$4$. Failure on all $3$ throws: $FFF$. Probability $P_4 = \frac{2}{3} 	imes \frac{2}{3} 	imes \frac{2}{3} = \frac{8}{27}$. Gain = $-20 - 20 - 20 = -₹ 60$.Expected gain $E = (40 	imes \frac{1}{3}) + (20 	imes \frac{2}{9}) + (0 	imes \frac{4}{27}) + (-60 	imes \frac{8}{27})$.$E = \frac{40}{3} + \frac{40}{9} + 0 - \frac{480}{27} = \frac{360 + 120 - 480}{27} = \frac{0}{27} = 0$.

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$0.1$	$0.2$	$0.3$	$0.4$

In a game,a man wins $₹ 40$ if he gets $5$ or $6$ on a throw of a fair die and loses $₹ 20$ for getting any other number on the die. If he decides to throw the die either until he gets a $5$ or $6$ or to a maximum of $3$ throws,then his expected gain/loss (in rupees) is:

Similar Questions

An unbiased die is tossed until a number greater than $4$ appears. The probability that an even number of tosses is needed is

The probability function of a discrete random variable $X$ is given by $P(X=r)=K r^2$, where $r=-2,-1,0,1,2,3$ and $K$ is a constant. The sum of the variance of $X$ and the square of the mean of $X$ is

The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$,then $P(X=0)$ is equal to:

$A$ random variable $X$ has the following probability distribution:
$X=x$ $1$ $2$ $3$ $4$
$P(X=x)$ $0.1$ $0.2$ $0.3$ $0.4$

The mean and standard deviation of $X$ are respectively:

Vedclass Test Series

Exam Paper Generator

Online Exam Module