Question

(15) Using Poisson distribution, find the probability that the king of diamond will be drawn
from a pack of well shuffled cards at least one in 156 consecutive trials.
(Given : e = 20)​

Answer 1

Step-by-step explanation:

sorry but don't have any answer for ur question

Answer 2

Given is a Poisson distribution for $156$ trials, Find the probability of drawing a king of diamond.

Explanation:

• The Poisson distribution is applied to data where the probability of the success of an event 'p' is much smaller than the number of trials 'n' that is, $p<. </li><li>The <strong>mean of the Poisson distribution </strong>is given by,<strong>  </strong>[tex]\lambda= np$  
• The PMF of this distribution is, $p(x)= \frac{\lambda^xe^{-\lambda}}{x!}$  
• Here we have 'x' is the number of times king of diamond appears.
• Therefore, the probability of success is , $p=\frac{1}{52}$
• Now it is given that $n=156\ \ \ \ ->\lambda= np= \frac{156}{52}=3$  
• Hence the PMF is , $p(x)=\frac{3^xe^{-3}}{x!}$
• Now for drawing a kind of diamond at least once, $x=0,1$  
•         ->$->p(x\leq 1)= p(0)+p(1)\\->p(x\leq 1)=\frac{3^0e^{-3}}{0!} +\frac{3^1e^{-3}}{1!}\\\\ ->p(x\leq 1)= \frac{1}{20^3} +\frac{3}{20^3} \ \ \ \ \ \ \ \ \ \ \ (Given\ e=20) \\->p(x\leq 1)=0.0005$    
• Probability of drawing a king of diamonds at least once is $0.0005$.