Solving Questions on Experimental Probability

Q. If a dice is thrown twice, find the probability of getting two 5's.

1. $\frac{1}{12}$
2. $\frac{1}{36}$
3. $\frac{1}{3}$

Q. In a showroom, there are $100$ cars. $10$ cars are black, $20$ cars are red, $15$ cars are blue, $25$ are white and $30$ are grey.

A car is chosen at random, what is the probability that it is a white car?

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

Q.

A bag has $13$ red, $14$ green and $15$ black balls. The probability of getting exactly $2$ blacks on pulling out $4$ balls is $p_1$. Now the number of each colour ball is doubled and $8$ balls are pulled out. The probability of getting exactly $4$ blacks is $p_2$. Then

1. $p_1<p_2$

2. $p_1=p_2$

3. $p_1>p_2$

4. None of these

Q. You roll a die $20$ times. Seven of those times, you get a $5$. What is the experimental probability of rolling a $5$?

1. $\frac{1}{20}$
   
2. $\frac{5}{20}$
   
3. $\frac{7}{20}$
   
4. $\frac{12}{20}$
   

Q. You asked your $3$ friends Marie, Dennis and Jack to toss a fair coin $12$ times each in a row and the outcomes of this experiment is given as below:

Coin Tossed by	Number of heads	Number of Tails
Marie	7	5
Dennis	6	6
Jack	8	4

Calculate the probability of occurence of heads for each individual.

1. Marie $=\frac{5}{12}$
   
   Dennis $=\frac{1}{2}$
   
   Jack $=\frac{1}{3}$
   
2. Marie $=\frac{7}{12}$
   
   Dennis $=\frac{1}{2}$
   
   Jack $=\frac{2}{3}$
   
3. Marie $=\frac{5}{12}$
   
   Dennis $=\frac{1}{2}$
   
   Jack $=\frac{2}{3}$
   
4. Marie $=\frac{7}{12}$
   
   Dennis $=\frac{1}{2}$
   
   Jack $=\frac{1}{3}$
   

Q. You flip a coin and get tails $35$ out of $70$ times. What is the experimental probability of flipping tails the next time around?

1. $25\%$
2. $50\%$
3. $75\%$
4. $35\%$

Q. The table given below shows the colors of jackets in a clothing store and their respective frequencies.

Color of jacket	Frequency
Blue	$20$
Black	$30$
Brown	$50$
Grey	$100$

If a jacket is picked at random, what color do you think it would be?

1. Blue
2. Black
3. Brown
4. Grey

Q.

A frequency distribution for the number of Nobel prize winners by the country for the years $1901-2001$ is given below:

Country	Winners
United States	$261$
United Kingdom	$79$
Germany	$61$
France	$28$
Soviet Union	$11$
Japan	$7$
Other countries	$57$

Suppose that a Nobel Prize recipient during the period $1901-2001$ is selected at random.

Find the probability that Nobel prize winner is from

a) Soviet Union

b) Either France or Germany

c) Any country other than the United States