Conduct the experiment flipping two coins 10 times and record the results in the frequency table below. Outcomes are sample spaces identified in task (b).
Outcomes Tally Frequency
HH IIIII/II 7
TT IIIII/ 5
HT II 2
TH IIIII/I 6
Total 20 20
Calculate the relative frequency for each outcome based on your results from task (e).
The relative frequency to HH is 7/20 The relative frequency of HT is 2/20 and the frequency for TH is 6/20 But TT had 5/20 witch is the theoretical frequency of HH,TH,HT,TT.
Compare the theoretical probability with the experimental relative frequency for flipping two tails. Are they the same?
No, they are not the same. The theoretical probability of flipping two tails in two-coin flips is 1/4 or 0.25, which means that in a large number of trials, we would expect two tails to occur 25% of the time. However, in this particular experiment where the coins were flipped 20 times, the experimental relative frequency of flipping two tails is not provided in the table.
Give reasons for differences between predicted and observed results.
As
Looking at your experimental outcomes in task (e), Explain why some results are higher than others.
Conduct the experiment flipping two coins 10 times and record the results in the frequency table below. Outcomes are sample spaces identified in task (b).
Outcomes Tally Frequency
HH IIIII/II 7
TT IIIII/ 5
HT II 2
TH IIIII/I 6
Total 20 20
Calculate the relative frequency for each outcome based on your results from task (e).
The relative frequency to HH is 7/20 The relative frequency of HT is 2/20 and the frequency for TH is 6/20 But TT had 5/20 witch is the theoretical frequency of HH,TH,HT,TT.
Compare the theoretical probability with the experimental relative frequency for flipping two tails. Are they the same?
No, they are not the same. The theoretical probability of flipping two tails in two-coin flips is 1/4 or 0.25, which means that in a large number of trials, we would expect two tails to occur 25% of the time. However, in this particular experiment where the coins were flipped 20 times, the experimental relative frequency of flipping two tails is not provided in the table.
Give reasons for differences between predicted and observed results.
As
Looking at your experimental outcomes in task (e), Explain why some results are higher than others.
The results for HH and TH are higher than HT because the combination of a head and a tail is more likely to occur than two heads or two tails in a coin flip. This is because there are two possible outcomes for each coin flip (heads or tails), so the probability of getting one of each is higher than getting two of the same outcome. Therefore, the results for HH and TH are more frequent than HT. The result for TT is lower than the others because it is the least likely combination to occur in a coin flip, and we only observed it 5 out of 20 trials.
h) Give reasons for differences between predicted and observed results.
The differences between predicted and observed results can be attributed to chance and random variation. The theoretical probabilities are based on mathematical calculations and assume that the coin flips are fair and unbiased. However, in reality, there may be small differences in the weight or shape of the coins, as well as differences in the force and angle of the flip, which can affect the outcome. Additionally, in a small sample size of only 20 coin flips, the observed frequencies may not perfectly match the theoretical probabilities due to chance variation. As the sample size increases, the observed results should converge towards the theoretical probabilities.
i) Looking at the experimental outcomes in task (e), Explain why some results are higher than others.
Some results are higher than others because of the different probabilities associated with each possible outcome. For example, the probability of getting one head and one tail (HT or TH) is 1/2 or 0.5, which is higher than the probability of getting two heads (HH) or two tails (TT), which is 1/4 or 0.25. Therefore, the outcomes of HT and TH are more likely to occur than HH or TT, which is reflected in the higher frequency of the former outcomes in the experimental results. The relative frequencies are a reflection of the observed outcomes, and they indicate the proportion of times each outcome occurred in the sample size of 20 flips.
Please complete cross word
Across
2. A possibility of an event
5. An expression showing equality
10. Opposite to addition
12. A board game where you purchase property and obtain money from other players
landing on your property.
13. A list of integers in order
14. The number of times something occurs
16. More than one cube marked on each side with one to six spots
18. Opposite to division
20. No order
22. Not biased
24. Collecting, interpreting and organising data
25. A subject using numbers and symbols
28. The top number of a fraction
29. At the end of a game where there is no winner
30. Positive or negative whole numbers
Down
1. Another word for con, fraud or hustle.
3. Mathematics involving letters or symbols
4. A competitive activity involving skill or chance.
6. Flipping a coin or rolling a die is an example of this type of event
7. A small part or segment
8. A piece of metal sometimes used to make a 50/50 decision
9. The bottom number of a fraction
11. Not certain
15. The number of ways to arrange an object where order is not important
17. How often something occurs or is likely to occur
19. A game in the UK where 6 balls are chosen at random from 1-49
21. A collection of measurements, observations or facts
23. To take a chance
26. There are usually 52 of these in four suits, as diamonds, hearts, spades, and clubs,
used in playing games of chance and skill.
27. Good fortune
Across
2. Probability
5. Equation
10. Subtraction
12. Monopoly
13. Sequence
14. Frequency
16. Dice
18. Multiplication
20. Random
22. Unbiased
24. Statistics
25. Mathematics
28. Numerator
29. Draw
30. Integers
Down
1. Scam
3. Algebra
4. Game
6. Random event
7. Segment
8. Coin
9. Denominator
11. Uncertain
15. Combination
17. Probability
19. Lottery
21. Data
23. Gamble
26. Cards
27. Luck
FIND THESE WORDS IN THE WORDSEARCH
cumulative frequency
interquartile range
frequency histogram
quantitative data
frequency polygon
qualitative data
random variable
expected value
weighted mean
sample space
statistics
parameter
statistic
midpoint
outlier
median
sample
event
range
mode
C X Q F S T A T I S T I C H M D H M N N G U J U
D X H R K Q P L Z W Y K H M Z Y U C H H K P G R
R Q W E S N U C J F O F T X W C T G K C G V S F
J I N Q V V J X Q N A E M D E T H G I E W V W N
P O L U A O N V Y F R A N D O M V A R I A B L E
N C U E X W E G N A R E L I T R A U Q R E T N I
O T S N E T I A N F L L Y U H E V E N T V U Q D
G S N C A V I E C A P S E L P M A S X H L W R I
Y A A Y E C D H W O J O B J U E L M D W V E C C
L T H H P C S E Y G T B W G V P K B W C T D X D
O A R I A Z P E U L A V D E T C E P X E P L I C
P D E S K L Q U A N T I T A T I V E D A T A H A
Y E I T S Z A Q E L Q U Z C M X F R R A N G E Z
C V L O Y C U M U L A T I V E F R E Q U E N C Y
N I T G N G S C M H B O Z Q F T L A J Z W F G O
E T U R A P T Z O G V R E O O G E Q B E O L Q B
U A O A I H D P D V V E S T A T I S T I C S N P
Q T V M D G U O E B V T X J G K G P A S T D Z E
E I S S E L X D J O S E Q T R M D I V S I N C M
R L U C M S A M P L E M B C N H C W N H H A R S
F A K Q G S D N Y O B A X S U Z C C G C U L K G
H U J B P Z D N C W N R K V Z Z W R B L L T H S
O Q D D R I V M O Y Q A T N I O P D I M C L H X
E O Q F N R R C F J O P O N L X N C O T G S I G