If X sim B(4, p) and 2 P(X=3)=3 P(X=2),then t | vedclass

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

Question

(A) Given $X \sim B(4, p)$,where $n=4$. The probability mass function is $P(X=k) = {}^{n}C_{k} p^{k} q^{n-k}$.Given the condition $2 P(X=3) = 3 P(X=2)

Vedclass · Accepted Answer

$\frac{9}{13}$

Vedclass · Answer

(A) Given $X \sim B(4, p)$,where $n=4$. The probability mass function is $P(X=k) = {}^{n}C_{k} p^{k} q^{n-k}$.Given the condition $2 P(X=3) = 3 P(X=2)$.Substituting the values: $2 	imes ({}^{4}C_{3} p^{3} q^{1}) = 3 	imes ({}^{4}C_{2} p^{2} q^{2})$.Calculating combinations: $2 	imes (4 p^{3} q) = 3 	imes (6 p^{2} q^{2})$.Simplifying: $8 p^{3} q = 18 p^{2} q^{2}$.Dividing both sides by $2 p^{2} q$ (assuming $p, q 
eq 0$): $4 p = 9 q$.Since $q = 1 - p$,we have $4 p = 9(1 - p)$.$4 p = 9 - 9 p$.$13 p = 9$.Therefore,$p = \frac{9}{13}$.

If $X \sim B(4, p)$ and $2 P(X=3)=3 P(X=2)$,then the value of $p$ is:

Similar Questions

Find the probability of throwing at most $2$ sixes in $6$ throws of a single die.

Let in a Binomial distribution,consisting of $5$ independent trials,probabilities of exactly $1$ and $2$ successes be $0.4096$ and $0.2048$ respectively. Then the probability of getting exactly $3$ successes is equal to

$A$ bag contains $30$ white balls and $10$ red balls. $16$ balls are drawn one by one randomly from the bag with replacement. If $X$ is the number of white balls drawn,then $\left( \frac{\text{mean of } X}{\text{standard deviation of } X} \right)$ is equal to

Two coins are tossed $5$ times. What is the probability of getting an odd number of heads?

$A$ coin is tossed $10$ times. The probability of getting exactly six heads is

Vedclass Test Series

Exam Paper Generator

Online Exam Module