Introduction to Experimental and Theoretical Probability

Q.

From $10000$ lottery tickets numbered from $1$to $10000$ one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$?

1. $\frac{1}{100}$

2. $\frac{1}{50}$

3. $\frac{1}{20}$

4. $\frac{1}{10}$

Q.

Of a total of $600$ bolts, $20\%$ are too large and $10\%$ are too small. The remaining are considered to be suitable. If a bolt is selected at random, the probability that it will be suitable is

1. $\frac{1}{5}$

2. $\frac{7}{10}$

3. $\frac{1}{10}$

4. $\frac{3}{10}$

Q. In which of the following scenario(s), we use experimental probability?

1. Forecasting weather
2. Prescribing right medication
3. Making bussiness decisions
4. Optimizing profits
5. All of the above

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.

Q. The probability that is based on the number of times the event has occured during the experiment and the total number of times the experiment was conducted is known as experimental probability.

1. True
2. False

Q.

A fair coin is tossed $60$ times and it came up with tails $27$ times. Find the probability of head.

Q. In a box full of red and green color marbles, there are $20$ red and $30$ green marbles. What is the theoretical probabilty that a blind-folded person draws a red marble on the first attempt?

1. $30$ out of $50$, which is $\frac{30}{50}$ or $\frac{3}{5}$
   
2. $20$ out of $50$, which is $\frac{20}{50}$ or $\frac{2}{5}$
   
3. $20$ out of $30$, which is $\frac{20}{30}$ or $\frac{2}{3}$
   
4. $50$ out of $50$, which is $\frac{50}{50}$ or $\frac{5}{5}$
   

Q. $\text{Probability}=\frac{\text{Number of successes}}{\text{Number of outcomes}}$-valid for both theoretical and experimental probabilities.

1. True
2. False

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. In a bowl there are $15$ first natural numbers. John chooses a number randomly $15$ times with replacement. All the outcomes are listed in the table below.

Outcomes	1	2	4	6	7	8	10	11	13	15
Number of times occurs	I	II	I	I	I	I	III	I	I	III

What is the experimental probability of choosing an even number?

1. $\frac{7}{15}$
2. $\frac{8}{15}$
3. $\frac{9}{15}$
4. None of the above

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. $\frac{6}{7}$