S.N. Chhibber Solutions for Chapter: Probability, Exercise 3: Revision Time

Two coins are tossed simultaneously $250$ times. The distribution of various outcomes is listed below.

Find the probability of each event and check that the sum of all probabilities is$1$.

In $20$ packets of $1$ kg sugar, the actual content of sugar is as follows (in kg):

$0.98, 0.95, 1.02, 1.05, 0.97, 0.92, 0.95, 0.90, 0.975, 1.05, 1.10, 1.15, 1.00, 1.02, 1.05, 1.00, 1.10, 1.05$$, \mathrm{0.96,} 1.005$

A packet is selected from the lot at random. If the probability that the packet containing $1$ kg sugar is $\frac{1}{x}$, then $x=$?

In $20$ packets of $1$ kg sugar, the actual content of sugar is as follows (in kg):

$0.98, 0.95, 1.02, \mathrm{1.05,} 0.97, 0.92, 0.95, 0.90, \mathrm{0.975,} \mathrm{1.05,} \mathrm{1.10,} \mathrm{1.15,} \mathrm{1.00,} \mathrm{1.02,} \mathrm{1.05,} \mathrm{1.00,} \mathrm{1.10,} 1.05$$, \mathrm{0.96,} 1.005$

A packet is selected from the lot at random. Find the probability that the packet contains less than $1$ kg sugar.

In $20$ packets of $1$ kg sugar, the actual content of sugar is as follows (in kg):

$0.98, 0.95, 1.02, \mathrm{1.05,} 0.97, 0.92, 0.95, 0.90, \mathrm{0.95,} \mathrm{0.975,} \mathrm{1.05,} \mathrm{1.10,} \mathrm{1.15,} \mathrm{1.00,} \mathrm{1.02,} \mathrm{1.05,} \mathrm{1.00,} \mathrm{1.10,} 1.05$$, \mathrm{0.96,} 1.005$

A packet is selected from the lot at random. Find the probability that the packet contains more than $1$ kg sugar.

A bag contains $5$ white marbles, $6$ red marbles and $9$ blue marbles. A marble is selected at random. What is the probability that the marble is not of blue colour.

Chits bearing numbers $25$ to $50$ are put in a box. A chit is drawn at random. If the simplest form of probability of getting a chit bearing a number which is a multiple of $7$ is $\frac{\mathrm{p}}{\mathrm{q}}$, then find the value of $\mathrm{p}+\mathrm{q}$.

Write the sample space when three coins are tossed simultaneously.