Embibe Experts Solutions for Chapter: Probability, Exercise 1: EXERCISE-1

If atleast one child in a family with $3$ children is a boy then the probability that $2$ of the children are boys, is -

$7$ persons are stopped on the road at random and asked about their birthdays. If the probability that $3$ of them are born on Wednesday, $2$ on Thursday and the remaining $2$ on Sunday is $\frac{K}{7^6}$, then $K$ is equal to -

A box has four dice in it. Three of them are fair dice but the fourth one has the number five on all of its faces. A die is chosen at random from the box and is rolled three times and shows up the face five on all the three occasions. The chance that the die chosen was a rigged die, is -

Mr. Dupont is a professional wine taster. When given a French wine, he will identify it with probability $0.9$ correctly as French and will mistake it for a Californian wine with probability $0.1$. When given a Californian wine, he will identify it with probability $0.8$ correctly as Californian and will mistake it for a French wine with probability $0.2$. Suppose that Mr. Dupont is given ten unlabelled glasses of wine, three with French and seven with Californian wines. He randomly picks a glass, tries the wine and solemnly says : "French". The probability that the wine he tasted was Californian, is nearly equal to -

A quadratic equation is chosen from the set of all quadratic equations which are unchanged by squaring their roots. The chance that the chosen equation has equal roots is -

$5$ persons entered the lift cabin on the ground floor of an $8$ floor building. Suppose that each of them independently and with equal probability, can leave the cabin at any other floor, starting from the first. The probability that all $5$ persons leave at different floors is -

$A \& B$ are two independent events such that $P\left(\overline{A}\right)=0.7, P\left(\overline{B}\right)=a \& P\left(A\cup B\right)=0.8$, then $a=$

A determinant is chosen at random from the set of all determinant of order $2$ with elements $0$ or $1$ only. The probability that the determinant chosen has the value non negative is -