A box of oranges is inspected by examining th | vedclass

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

Question

(A) Let $A, B,$ and $C$ be the events that the first,second,and third drawn oranges are good,respectively.The probability that the first orange drawn

Vedclass · Accepted Answer

$\frac{44}{91}$

Vedclass · Answer

(A) Let $A, B,$ and $C$ be the events that the first,second,and third drawn oranges are good,respectively.The probability that the first orange drawn is good is $P(A) = \frac{12}{15}$.Since the oranges are drawn without replacement,the total number of oranges and the number of good oranges decrease by $1$ for each subsequent draw.The probability that the second orange is good,given the first was good,is $P(B|A) = \frac{11}{14}$.The probability that the third orange is good,given the first two were good,is $P(C|A \cap B) = \frac{10}{13}$.The box is approved for sale if all three oranges are good. Thus,the required probability is $P(A \cap B \cap C) = P(A) 	imes P(B|A) 	imes P(C|A \cap B)$.$P(A \cap B \cap C) = \frac{12}{15} 	imes \frac{11}{14} 	imes \frac{10}{13} = \frac{4}{5} 	imes \frac{11}{14} 	imes \frac{10}{13} = \frac{440}{910} = \frac{44}{91}$.Therefore,the probability that the box is approved for sale is $\frac{44}{91}$.

Similar Questions

For independent events $A$ and $B$,if $P(A) = p$,$P(B) = \frac{1}{2}$,and $P(A \cup B) = \frac{3}{5}$,then find the value of $p$.

An urn contains $4$ red and $5$ white balls. Two balls are drawn one after the other without replacement,then the probability that both the balls are red is

$A$ bag $X$ contains $2$ white and $3$ black balls and another bag $Y$ contains $4$ white and $2$ black balls. One bag is selected at random and a ball is drawn from it. Then,the probability for the ball chosen to be white is:

$A$ bag contains $10$ similar balls,of which $4$ are blue and $6$ are red. Three balls are taken out at random from the bag one after the other without replacement. The probability that all the three balls drawn are red is

Vedclass Test Series

Exam Paper Generator

Online Exam Module