S3 Probability and Statistics

Question 1

What is probability?

Answer 1

The probability of an event is a number indicating how likely it would happen. It is notated by P(E) / the probability of an event E.

Question 2

What is the sample space?

Answer 2

The collection or list of all possible outcomes.

Question 3

What is the range of values of the probability of an event?

Answer 3

P(E) must be between 0 and 1, inclusive. If P(E)=0, that means E is impossible to occur (impossible event). If P(E)=1, that means E must occur (certain event).

Question 4

In a set of playing cards, what is the probability that a card drawn is a red number card or a face card of clubs?

Answer 4

total number of cards = 13 x 4 = 52
number of red number cards = 9 x 2 = 18
number of face cards of clubs = 3
number of cards that are both red number cards and clubs face cards = 0
probability = (18 + 3)/52 = 21/52

Question 5

In a set of playing cards, what is the probability that the card drawn is a black diamond number card?

Answer 5

0: diamond cards must be red.

Question 6

P(E)=?

Answer 6

Number of favourable outcomes/ number of total outcomes

Question 7

In a game, a fair dice is thrown. $10 is awarded if the number obtained is a prime and $15 is lost if the number obtained is 6. If we have to pay $5 to play this game, should we play this game?

Answer 7

expected return value: $10 x 3/6 + ($-15) x 1/6 =
$2.5
expected total gain = $2.5 - $5 = $-2.5, expected to lose money through the game
no, we should not play the game.

Question 8

What is the mean?

Answer 8

The mean, or the average/arithmetic mean, is denoted by bar x and calculated by the sum of data over the number of data.

Question 9

What is the median?

Answer 9

The median is the value in the middle of a set of data arranged in ascending or descending order. For an odd number of data, the median is one of the data; for an even number of data, the median is the average of the middle two data.

Question 10

What is the mode?

Answer 10

The mode is the datum that appears the most frequently. There may be one mode, multiple modes, or no mode (when every datum appears for the same number of times).

Question 11

What is the modal class?

Answer 11

The modal class is the class interval with the highest frequency.

Question 12

What is the difference between 25th percentile and upper quartile?

Answer 12

25th percentile: the data ranking 25% of the total number of data in ascending order
upper quartile: the data at the higher 25% of the total number of data/ ranking 75% in all data in ascending order