4 bad apples are mixed accidentally with 20 good apples. Obtain the probability distribution of the numbers of bad apples in a draw of 2 apples at random


Question and Answers Forum

All Questions Topic List
Probability and Statistics Questions
Previous in All Question Next in All Question
Previous in Probability and Statistics Next in Probability and Statistics
Question Number 147906 by Odhiambojr last updated on 24/Jul/21

$4 b a d a p p l e s a r e m i x e d a c c i d e n t a l l y$ $w i t h 20 g o o d a p p l e s . O b t a i n t h e$ $p r o b a b i l i t y d i s t r i b u t i o n o f t h e$ $n u m b e r s o f b a d a p p l e s i n a d r a w o f$ $2 a p p l e s a t r a n d o m$
	Answered by Olaf_Thorendsen last updated on 24/Jul/21
	$Let X be the probability of bad apples in a draw. Then X is a random variable with values 0, 1 and 2. Total apples are 4 Bad apples (B) + 20 Good apples (G) = 24. • P(X=0) is the probability of no bad apple in a draw of two apples. P(X=0) = (C_2 ^(20) /C_2 ^(24) ) = ((20×19)/(24×23)) = ((95)/(138)) • Similary P(X=1) = ((C_1 ^4 C_1 ^(20) )/C_2 ^(24) ) = ((40)/(138)) • P(X=2) = (C_2 ^4 /C_2 ^(24) ) = ((4×3)/(24×23)) = (3/(138)) Therefore, the probability distribution of X is : { ((P(X=0) = ((95)/(138)))),((P(X=1) = ((40)/(138)))),((P(X=2) = (3/(138)))) :}$
	$Let X be the probability of bad apples$ $in a draw . Then X is a random$ $variable with values 0, 1 and 2 .$ $Total apples are 4 Bad apples (B) +$ $20 Good apples (G) = 24 .$ $∙ P (X = 0) is the probability of no bad$ $apple in a draw of two apples .$ $P (X = 0) = \frac{C_{2}^{20}}{C_{2}^{24}} = \frac{20 \times 19}{24 \times 23} = \frac{95}{138}$ $∙ Similary P (X = 1) = \frac{C_{1}^{4} C_{1}^{20}}{C_{2}^{24}} = \frac{40}{138}$ $∙ P (X = 2) = \frac{C_{2}^{4}}{C_{2}^{24}} = \frac{4 \times 3}{24 \times 23} = \frac{3}{138}$ $Therefore, the probability distribution$ $of X is :$ ${\begin{cases} P (X = 0) = \frac{95}{138} \\ P (X = 1) = \frac{40}{138} \\ P (X = 2) = \frac{3}{138} \end{cases}$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum