G Tewani Solutions for Chapter: Probability II, Exercise 1: Exercises

One ticket is selected at random from $100$ tickets numbered $00, 01, 02, \dots .98, 99$. If $x_1$ and $x_2$ denotes the sum and product of the digits on the tickets, then $P\left(\frac{\left(x_1=9\right)}{\left(x_2=0\right)}\right)$ is equal to

Let $A$ and $B$ are events of an experiment and $P\left(A\right)=\frac{1}{4}, P\left(A\cup B\right)=\frac{1}{2}$, then value of $P\left(\frac{B}{A^C}\right)$ is

All the jacks, queens, kings and aces of a regular $52$ cards deck are taken out. The $16$ cards are thoroughly shuffled and my opponent, a person who always tells the truth, simultaneously draws two cards at random and says, 'I hold at least one ace'. The probability that he holds two aces is

Five horses are in a race. Mr. $\mathrm{A}$ selects two of the horses at random and bets on them. The probability that Mr. $\mathrm{A}$ selected the winning horse, is

If odds against solving a question by three students are $2:1, 5:2$ and $5:3$, respectively, then probability that the question is solved only by one student is

A dice is thrown a fixed number of times. If the probability of getting even number $3$ times is the same as the probability of getting even number $4$ times, the probability of getting an even number exactly once is

$A$ speaks truth in $60\%$ cases and $B$ speaks truth in $70\%$ cases. The probability that they will say the same thing while describing single event, is

A purse contains $2$ six-sided dice. One is a normal fair die, while the other has two $1^{\text{'}}\text{s},$ two $3^{\text{'}}\text{s},$ and two $5^{\text{'}}\text{s}$. A die is picked up and rolled. Because of some secret magnetic attraction of the unfair die, there is $75\%$ chance of picking the unfair die and a $25\%$ chance of picking a fair die. The die is rolled and shows up the face $3$. The probability that a fair die was picked up is