Solving Questions on Theoretical Probability

Q. A spinner is divided into eight equal sectors, numbered from $1$ to $8$. What is the probability of spinning a number that is a multiple of $3$?

1. $\frac{1}{2}$
   
2. $\frac{1}{3}$
   
3. $\frac{1}{8}$
   
4. $\frac{1}{4}$
   

Q. The record of weather stations report shows that out of the past $100$ consecutive days, its weather forecast was correct $35$ times. Find the probability that on a given day it was not correct.

1. $\frac{13}{20}$
   
2. $\frac{7}{20}$
   
3. $\frac{11}{20}$
   
4. $\frac{1}{20}$
   

Q.

In a cricket match, a batsman hits a boundary $4$ times out of the $32$ balls he plays. In a given ball, what is the probability that he does not hit the boundary?

1. $\frac{1}{8}$

2. $\frac{1}{7}$

3. $\frac{7}{8}$

4. $\frac{6}{8}$

Q. Match the colors with their respective probabilities for the spin landing on a particular color.

1. Yellow
2. Red + Blue
3. Red+Blue+Green
4. $\frac{1}{2}$
5. $\frac{1}{4}$
6. $\frac{3}{4}$

Q. A bag contains $15$ red marbles, $5$ green marbles and $10$ yellow marbles. If Alex picks up a marble at random, then find the theoretical probability that it is a green marble.

1. $\frac{1}{2}$
   
2. $\frac{1}{3}$
   
3. $\frac{1}{6}$
   
4. $1$

Q. Find the probability of rolling an odd number when you roll an ordinary die. Express this probability as a percent.

1. $\frac{1}{2}$ or $50\%$
   
2. $\frac{1}{3}$ or $33.3\%$
   
3. $\frac{1}{4}$ or $25\%$
   
4. $\frac{1}{5}$ or $20\%$
   

Q. From the table below, plot the probability distribution graph of rainfall in a city. The probability of rainfall occuring in April is

1. 0.2
2. 0.25
3. 0.1