Introduction to Experimental and Theoretical Probability

Q.

A dice is thrown ten times. If getting an even number is considered a success, then the probability of four successes is

1. ${}^{10}C_4{\left(\frac{1}{2}\right)}^4$

2. ${}^{10}C_4{\left(\frac{1}{2}\right)}^6$

3. ${}^{10}C_4(\frac{1}{2}{)}^8$

4. ${}^{10}C_4(\frac{1}{2}{)}^{10}$

Q.

A fair coin is tossed $n$ times. If the probability that head occurs $6$ times is equal to the probability that head occurs $8$ times, then $n$ is equal to

1. $15$

2. $14$

3. $12$

4. $7$

Q.

Eleven books consisting of $5$ Mathematics, $4$ Physics, and $2$ Chemistry are placed on a shelf. The number of possible ways of arranging them on the assumption that the books of the same subject are all together is?

1. $4!2!$

2. $11!$

3. $5!4!3!2!$

4. None of these

Q.

Apoorv throws two dice once and computes the product of the numbers appearing on the dice. Peehu throws one die and squares the number that appears on it. Who has the better chance of getting the number $36$? Why?

Q.

How do you find the probability of getting a red face card in a deck of $52$ cards?

Q.

How might one lessen uncertainty?

Q.

Four numbers are chosen at random from $\{1,2,3,......,40\}$.

The probability that they are not consecutive, is

1. $\frac{1}{2470}$

2. $\frac{4}{7969}$

3. $\frac{2469}{2470}$

4. $\frac{7965}{7969}$

Q.

A fair coin is tossed a fixed number of items. If the probability of getting $7$ heads is equal to that of getting $9$ heads, then the probability of getting$3$ heads is

1. $\frac{35}{2^{12}}$

2. $\frac{35}{2^{14}}$

3. $\frac{7}{2^{12}}$

4. None of these

Q. Given the data of whether or not rain occurs when there is cloudy weather, what is the probability of rain occuring on a cloudy day?

1. $\frac{1}{2}$
2. $\frac{3}{4}$
3. $\frac{2}{3}$
4. $\frac{5}{8}$

Q. Consider an experiment of rotating a spinner $40$ times. The table given below shows the results of the experiment conducted. Find the experimental probability of spinning the color - Orange.

Color	Occurances
Orange	$8$
Green	$12$
Blue	$5$
Yellow	$15$

1. $\frac{1}{8}$
   
2. $\frac{3}{10}$
   
3. $\frac{1}{5}$
   
4. $\frac{3}{8}$
   

Q. A process that has a well-defined collection of outcomes is called an experiment.

1. True
2. False

Q. Charlie flipped a coin $80$ times and gets heads $25$ times. What is the experimental probability of getting tails?

1. $\frac{5}{16}$
   
2. $\frac{5}{11}$
   
3. $\frac{11}{16}$
   

Q. Find the theoretical probability of getting a $2$ in a fair die throw.

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

Q. Pastries made by Marie in the previous week from Monday to Sunday are
$5,6,3,4,7,8,9$ respectively.

On the basis of this data, calculate the experimental probability that Marie prepares less than $7$ pastries for the previous week.

1. $\frac{3}{7}$
   
2. $\frac{4}{7}$
   
3. $\frac{5}{7}$
   
4. $\frac{6}{7}$
   

Q. A fair, unbiased coin is just as likely to land on one side as landing on the other.

1. True
2. False

Q. What is an experiment? Choose the most suitable option.

Q. In both experimental and theoretical probability, the probability of a favorable event can be given by which of the following?

1. $\frac{\text{Total Outcomes}}{\text{Favourable outcomes}}$
2. $\frac{\text{Total Outcomes}}{\text{Unfavorable outcomes}}$
3. $\frac{\text{Favorable outcomes}}{\text{Total Outcomes}}$
4. $\frac{\text{Unfavorable outcomes}}{\text{Total Outcomes}}$

Q. Which among the following is an example of theoretical probability?

1. A coin is tossed $20$ times and it is recorded that heads occurred $8$ times and tails occurred $12$ times.
2. A coin is tossed.