There are $10$ coins in a box, out of which $8$ are normal and the remaining are with heads on both sides. $A$ coin is chosen at random from the box and tossed $6$ times. If it shows heads each time, then the probability that the selected coin has heads on both sides is

$A$ student appears for a quiz consisting of only true-false type questions and answers all the questions. The student knows the answers of some questions and guesses the answers for the remaining questions. Whenever the student knows the answer of a question,he gives the correct answer. Assume that the probability of the student giving the correct answer for a question,given that he has guessed it,is $\frac{1}{2}$. Also assume that the probability of the answer for a question being guessed,given that the student's answer is correct,is $\frac{1}{6}$. Then the probability that the student knows the answer of a randomly chosen question is

In a certain college, $4 \%$ of men and $1 \%$ of women are taller than $1.8 \ m$. Also, $60 \%$ of students are women. If a student selected at random is found to be taller than $1.8 \ m$, then the probability that the student is a woman is: (in $/ 11$)

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 $P(A|L)$?

In a college,$25\%$ of the boys and $10\%$ of the girls offer Mathematics. The girls constitute $60\%$ of the total number of students. If a student is selected at random and is found to be studying Mathematics,the probability that the student is a girl,is

$A, B_1, B_2, B_3$ are the events in a random experiment. If $P(B_1)=0.25, P(B_2)=0.30, P(B_3)=0.45, P(A|B_1)=0.05, P(A|B_2)=0.04, P(A|B_3)=0.03$, then $P(B_2|A) = $