A fair coin is tossed four times. A person wi | vedclass

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

Question

Since the coin is tossed four times,there are $2^4 = 16$ possible outcomes.Let $H$ be the number of heads and $T$ be the number of tails,where $H + T

Vedclass · Accepted Answer

Vedclass · Answer

Since the coin is tossed four times,there are $2^4 = 16$ possible outcomes.
Let $H$ be the number of heads and $T$ be the number of tails,where $H + T = 4$.
The gain/loss $G$ is given by $G = 1(H) - 1.50(T)$.
$1$. If $H=4, T=0$: $G = 1(4) - 1.50(0) = Rs. 4.00$. Number of outcomes = $\binom{4}{4} = 1$. Probability = $\frac{1}{16}$.
$2$. If $H=3, T=1$: $G = 1(3) - 1.50(1) = Rs. 1.50$. Number of outcomes = $\binom{4}{3} = 4$. Probability = $\frac{4}{16} = \frac{1}{4}$.
$3$. If $H=2, T=2$: $G = 1(2) - 1.50(2) = 2 - 3 = -Rs. 1.00$. Number of outcomes = $\binom{4}{2} = 6$. Probability = $\frac{6}{16} = \frac{3}{8}$.
$4$. If $H=1, T=3$: $G = 1(1) - 1.50(3) = 1 - 4.50 = -Rs. 3.50$. Number of outcomes = $\binom{4}{1} = 4$. Probability = $\frac{4}{16} = \frac{1}{4}$.
$5$. If $H=0, T=4$: $G = 1(0) - 1.50(4) = -Rs. 6.00$. Number of outcomes = $\binom{4}{0} = 1$. Probability = $\frac{1}{16}$.

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X)$	$0$	$k$	$2k$	$3k$	$3k^2$	$k^2$	$2k^2$	$7k^2+k$

$X$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$k$	$2k$	$4k$	$k$

Number of smart phones $(x)$	$0$	$1$	$2$	$3$	$4$	$5$
Probability $(P(x))$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

$A$ fair coin is tossed four times. $A$ person wins $Rs. 1$ for each head and loses $Rs. 1.50$ for each tail that turns up. From the sample space,calculate the different amounts of money one can have after four tosses and the probability of having each of these amounts.

Similar Questions

In a game,$3$ coins are tossed. $A$ person is paid ₹ $7$ if he gets all heads or all tails,and he is supposed to pay ₹ $3$ if he gets one head or two heads. The amount he can expect to win on an average per game is ₹

$A$ random variable $X$ has the following probability distribution:

$X$ $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$

$P(X)$ $0$ $k$ $2k$ $3k$ $3k^2$ $k^2$ $2k^2$ $7k^2+k$

Determine $P(X < 3)$. (in $/10$)

$A$ coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed twice,find the probability distribution of number of tails.

The probability distribution of a discrete random variable $X$ is given by the table below:
$X$ $0$ $1$ $2$ $3$ $4$
$P(X=x)$ $2k$ $k$ $2k$ $4k$ $k$

If $a = P(X < 3)$ and $b = P(2 < X < 4)$,then:

The following table shows the probability distribution of smart phones sold in a shop per day:
Number of smart phones $(x)$ $0$ $1$ $2$ $3$ $4$ $5$
Probability $(P(x))$ $k$ $0.3$ $0.15$ $0.15$ $0.1$ $2k$

Then $E(x) = ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module