Frequency of an Event, Relative Frequency and Experimental Probability

Q. The number of times an event occurs is known as the frequency of that event.

1. True
2. False

Q. Outcome is a possible result of an experiment or trial.

1. True
2. False

Q.
Given the above outcomes of 100 coin tosses, what is the experimental probability of flipping a head and a tail respectively?

1. $P\left(Head\right)=0.6$
   $P\left(Tail\right)=0.4$
2. $P\left(Head\right)=0.40$
   $P\left(Tail\right)=0.60$
3. $P\left(Head\right)=0.5$
   $P\left(Tail\right)=0.5$
4. None of the above

Q.

How do you calculate experimental probability?

Q. Markus asks some people in his town about their dietary habits and records the results as shown in the table given below:

Dietary Habits	Frequency
Vegetarian	$56$
Non-vegetarian	$44$

Find the relative frequency of a person in town being non-vegetarian.

1. $\frac{56}{100}$
   
2. $\frac{56}{44}$
   
3. $\frac{44}{56}$
   
4. $\frac{44}{100}$
   

Q.

In a particular city, there were 152 cloudy days last year and it rained on 95 of those days. What is the relative frequency of no rain on a cloudy day in that city?

1. $\frac{16}{19}$
2. $\frac{95}{152}$
3. $\frac{5}{8}$
4. $\frac{3}{8}$

Q.
Given the above outcomes of $100$ coin tosses of a fair coin, what is the theoretical probability of flipping a head or a tail?

1. $P\left(Head\right)=P\left(Tail\right)=0.5$
2. $P\left(Head\right)=0.44$
   $P\left(Tail\right)=0.56$
3. $P\left(Head\right)=0.56$
   $P\left(Tail\right)=0.44$
4. None of the above

Q. In a particular city, there were $136$ cloudy days last year and it rained on $102$ of those days. What is the relative frequency of rain on a cloudy day in that city?

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

Q. A coin is tossed 80 times and 45 of those times it lands heads up. What is the experimental probability of flipping a head in the next toss?

1. $P\left(Head\right)=\frac{7}{16}$
2. $P\left(Head\right)=\frac{1}{2}$
3. $P\left(Head\right)=\frac{9}{16}$
4. $P\left(Head\right)=\frac{11}{16}$

Q. It is estimated that $60\%$ of kids like milkshakes and $70\%$ of kids like to go to the park to play. Using a simulator that generates random two-digit numbers using the digits 0 through 9, estimate the probability that a random kid will not like milkshakes and does not like to go to the park to play.
Note: The ones place of a two-digit number and 1 through 6 represents kids who like milkshakes.
The tens place of the two-digit number and 1 through 7 represents kids liking to go to the park to play.

26	32	64	08	66	11	76	01	79	67
22	61	87	72	53	49	59	81	68	19
94	78	38	56	42	77	19	48	20	05
02	80	85	82	54	43	69	12	21	91
76	46	98	14	40	45	56	64	97	92

1. $8\%$
2. $12\%$
3. $6\%$
4. $15\%$

Q. Experimental probability is determined on the basis of the observations or the results of an experiment repeated many times.

1. True
2. False

Q. Stacey bought a pack of lettuce seeds. She planted 50 of those seeds out of which only 23 grew into plants. What is the probability that the next seed she plants will grow into a plant?

1. $P\left(Germination\right)=\frac{2}{5}$
2. $P\left(Germination\right)=\frac{23}{50}$
3. $P\left(Germination\right)=\frac{27}{50}$
4. None of the above

Q. A ball was picked at random from a bag of red and black balls 23 times. 13 of the picked balls were red and remaining were black. What are the relative frequencies of picking black balls and red balls respectively?

1. $\frac{10}{23}$, $\frac{13}{23}$
2. $\frac{13}{23}$, $\frac{10}{23}$
3. $\frac{23}{13}$, $\frac{23}{10}$
4. $\frac{23}{10}$, $\frac{23}{13}$

Q. The relative frequency of an event can be written as which of the following?

1. $\frac{\text{Event frequency}}{\text{Total trials}}$
2. $\frac{\text{Total trials}}{\text{Event frequency}}$
3. $\frac{\text{Total trials}}{\text{Total events}}$
4. None of the above

Q. A ball was picked at random from a bag of red and black balls 13 times. 6 of the picked balls were red and remaining were black. Which ball has a greater chance of being picked on the ${14}^{th}$ pick?

1. Red Marble
2. Black Marble
3. Both are Equally Likely to be picked.

Q. Suppose you have a pack of $52$ cards. In $12$ attempts, you pick a red card $5$ times. Find the relative frequency for picking the red card.

Also, find the probability $\text{P(B)}$ of drawing a black card.

1. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
   
   $\text{P(B)}=\frac{1}{2}$
   
2. $\text{Relative frequency for the red card}$ $=\frac{12}{5}$
   
   $\text{P(B)}=\frac{1}{2}$
   
3. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
   
   $\text{P(B)}=\frac{1}{3}$
   
4. $\text{Relative frequency for the red card}$ $=\frac{5}{12}$
   
   $\text{P(B)}=\frac{1}{4}$
   

Q. Theoretical and Experimental probabilites need not be the same if we conduct an experiment a small number of times.

1. True
2. False

Q. It is estimated within a group of people that $80\%$ people have health insurance, $90\%$ people have tea in the morning, and $60\%$ people exercise regularly. Using the simulator that generates random three-digit numbers using digits from 0 through 9, work out the probability that the person chosen has health insurance, drinks tea in the morning, and exercises everyday.
Note: The ones place of a three-digit number and 1 through 6 represents people doing regular exercise.
The tens place of the three-digit number and 1 through 9 represents people who drink tea.
The hundreds place of the three-digit number and 1 through 8 represents people having health insurance.

Simulator:

842	242	075	572	711	632	874	576	641	884
833	415	871	381	335	984	652	495	663	426
415	323	904	784	947	546	236	316	565	631
693	696	726	714	226	265	815	835	235	051
654	814	895	824	424	425	152	531	078	998

1. $96\%$
2. $60\%$
3. $84\%$
4. $86\%$

Q. It is expected that there is a $60\%$ chance that a bike will be sold in a showroom at any given day. From the simulation using digits from 1 through 5 and 50 trials, determine the estimated probability of at least two bikes sold out of three consecutive days.
Simulated data shows the following:
$123,125,451,523,542,452,124,134,234,325,432,243,542,453,421,431,145,341,441,552,343,215,252,114,222,245,314,225,331,152,411,423,313,251,542,551,442,451,542,443,415,514,454,545,214,215,542,555,514,545$.
Note: Take 1, 2, and 3 representing bikes that are sold.

1. $54\%$
2. $60\%$
3. $57\%$
4. $59\%$

Q. The formula of relative frequency is

1. $\frac{\text{Total frequency}}{\text{Subgroup frequency}}$
   
2. $\frac{\text{Total frequency}}{\text{Total frequency}}$
   
3. $\frac{\text{Subgroup frequency}}{\text{Subgroup frequency}}$
   
4. $\frac{\text{Subgroup frequency}}{\text{Total frequency}}$
   

Q. Alexa has a packet containing $30$ chocolates. Her favorites are the blue and the green ones. The table below shows the frequency of each different chocolate selected as she picked all $30$ chocolates one-by-one and finished them all.

Chocolate color	Red	Yellow	Blue	Green
Frequency	9	5	6	10

What is the relative frequency of the chocolate picked up by Alexa to be one of her favorites ?

1. $\frac{7}{15}$
   
2. $\frac{11}{30}$
   
3. $\frac{1}{2}$
   
4. $\frac{8}{15}$