$A$ manufacturer has three machine operators $A$,$B$,and $C$. The first operator $A$ produces $1 \%$ defective items,whereas the other two operators $B$ and $C$ produce $5 \%$ and $7 \%$ defective items respectively. $A$ is on the job for $50 \%$ of the time,$B$ is on the job for $30 \%$ of the time,and $C$ is on the job for $20 \%$ of the time. If a defective item is produced,what is the probability that it was produced by $A$ (in $/34$)?

In a certain recruitment test with multiple-choice questions, there are four options for each question, out of which only one is correct. An intelligent student knows $90 \%$ of the correct answers, while a weak student knows only $20 \%$ of the correct answers. If a weak student gets the correct answer, what is the probability that they were guessing?

Recent studies suggest that $12\%$ of the world population is left-handed. Depending on parents' hand usage, the chances of having left-handed children are as follows: $A$. Both parents are left-handed, chances of having left-handed children = $24\%$. $B$. Both parents are right-handed, chance of having left-handed children = $9\%$. $C$. Father left-handed and mother right-handed, chances of having left-handed children = $17\%$. $D$. Father right-handed and mother left-handed, chances of having left-handed children = $22\%$. Given $P(A) = P(B) = P(C) = P(D) = 1/4$ and $L$ denotes the event that the child is left-handed. What is the probability $P(A|L)$?

$A$ dealer gets refrigerators from $3$ different manufacturing companies $C_1, C_2$ and $C_3$. $25 \%$ of his stock is from $C_1, 35 \%$ from $C_2$ and $40 \%$ from $C_3$. The percentages of receiving defective refrigerators from $C_1, C_2$ and $C_3$ are $3 \%, 2 \%$ and $1 \%$ respectively. If a refrigerator sold at random is found to be defective by a customer, then the probability that it is from $C_2$ is

Bag $I$ contains $3$ red and $4$ black balls. Bag $II$ contains $5$ red and $6$ black balls. If one ball is drawn at random from one of the bags, and it is found to be red, then the probability that it was drawn from Bag $II$, is

Three similar urns $A, B, C$ contain $2$ red and $3$ white balls; $3$ red and $2$ white balls; $1$ red and $4$ white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is