Three screws are drawn at random from a lot o | vedclass

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

Question

(A) Total screws $= 50$.Defective screws $= 5$.Non-defective screws $= 45$.Let $A$ be the event that all $3$ screws drawn are non-defective.$(a)$ With

Vedclass · Accepted Answer

$\left(\frac{9}{10}\right)^3, \frac{1419}{1960}$

Vedclass · Answer

(A) Total screws $= 50$.Defective screws $= 5$.Non-defective screws $= 45$.Let $A$ be the event that all $3$ screws drawn are non-defective.$(a)$ With replacement:The probability of drawing a non-defective screw in one draw is $P = \frac{45}{50} = \frac{9}{10}$.Since the drawing is with replacement,the events are independent.$P(A) = \left(\frac{9}{10}ight) 	imes \left(\frac{9}{10}ight) 	imes \left(\frac{9}{10}ight) = \left(\frac{9}{10}ight)^3$.$(b)$ Without replacement:The probability is calculated as:$P(A) = \frac{45}{50} 	imes \frac{44}{49} 	imes \frac{43}{48}$.$P(A) = \frac{9}{10} 	imes \frac{44}{49} 	imes \frac{43}{48} = \frac{3}{10} 	imes \frac{11}{49} 	imes \frac{43}{4} = \frac{1419}{1960}$.

Three screws are drawn at random from a lot of $50$ screws containing $5$ defective ones. The probability of the event that all $3$ screws drawn are non-defective,assuming that the drawing is $(a)$ with replacement and $(b)$ without replacement,is respectively:

Similar Questions

If $7$ dice are thrown simultaneously,then the probability that all six digits appear on the upper faces is equal to -

$A$ bag contains $n + 1$ coins. Among these coins,one coin has heads on both sides,while all other coins are fair. $A$ coin is chosen at random from the bag. If the probability of getting a head when the chosen coin is tossed is $7/12$,what is the value of $n$?

$A$ and $B$ are independent events with $P(A)=\frac{3}{10}$ and $P(B)=\frac{2}{5}$. Then,the value of $P(A^{\prime} \cup B)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module