Theoretical Probability
A fair coin is tossed 20 times. What is the theoretical probability of obtaining heads? Simplify your answer.
P(H) = 1/2
A die is rolled 10 times. A frequency table of the ourcomes is shown below.
Outcome 1 | 2 | 3 | 4 | 5 | 6
Frequency 3 | 1 | 1 | 1 | 0 | 4
What is the relative frequency of rolling a 6? Write your answer in correct notation.
P(6) = 4/10 = 2/5
Use the two-way table below to determine how many students were surveyed.
| Soccer | Tennis |
Boys | 5 | 20 | 25
Girls | 10 | 3 | 13
| 15 | 23 | 38
38 total.
Explain what U and N mean when used in probability annotation.
U is the union of two sections, it can be said as 'or'.
N is the intersection and can be replaced with the word 'and'.
To calculate the probability of two events happening, you should use which formula?
a) P(ANB)= P(A) / P(B)
b) P(AUB)=P(A) X P(B)
c) P(ANB)=P(A) X P(B)
d) P(AUB)=P(A) + P(B)
c) P(ANB)=P(A) X P(B)
A fair die is rolled. What is the probability of obtaining a number less than 5? Simplify your answer.
P(<5) = 2/3
If event (A) is your test falling on a Friday, list the complement of that event using correct notation.
A' = Monday, Tuesday, Wednesday, Thursday, Saturday, Sunday.
Using the table, what is the probability that a boy likes tennis?
| Soccer | Tennis |
Boys | 5 | 20 | 25
Girls | 10 | 3 | 13
| 15 | 23 | 38
20/38
= 10/19
Shade the region AUB.
Teacher to correct on board.
Teacher to correct answer.
List the sample space of drawing from a deck of cards and noting the suit. Use correct notation.
S = {hearts, diamonds, spades, clubs}
A spinner numbered 1-4 was spun a certain number of times and the following results were achieved.
Outcome 1 | 2 | 3 | 4
Frequency 7 | 26 | 9 | 58
How many trials were conducted?
100 trials
(add all the frequencies)
| Girls | Boys |
Footy | 36 | 54 | 90
Footy' | 18 | 12 | 30
| 54 | 66 | 120
Calculate the probability of A'NB' using the music Venn Diagram displayed on the TV.
P(A'NB') = 38/108
= 19/54
A bag containing mixed nuts is shared among friends. There are 10 macadamias, 5 cashews, and 15 peanuts. What is the probability of the first and second friend both choosing and eating a peanut?
7/29
The sum of all probabilities, theoretical and experimental should equal ___?
1
At a birthday party, some cans of soft drink were put in a container of ice. There were 16 cans of Coke, 20 cans of Sprite, 13 cans of Fanta, 8 cans of Sunkist and 15 cans of Pepsi.
If a can was picked at random, what is the probability that it was not a can of Fanta?
59/72
P(F') = 1 - P(F)
or P(C) + P(S) + P(Su) + P(P)
Use the table below to determine what is the probability the girls surveyed are right handed?
| Left Handed | Right Handed |
Boys | 17 | | 35
Girls | | |
| 29 | | 70
P(GNR) = 23/70
Show the apples and bananas Venn diagram in a two-way table.
| A | A' |
B | 7 | 10 | 17
B' | 12 | 4 | 16
| 19 | 14 | 33
A bag contains 4 red and 6 yellow balls. If the first ball drawn is yellow, explain the difference in the probability of drawing the second ball if the first ball was replaced compared to not being replaced.
If the first ball is replaced, the probability of drawing a yellow ball stays the same on the second draw, i.e. (6/10)
If the first ball isn’t replaced, the probability of drawing a yellow ball on the second draw decreases, i.e. (5/9)
Which of these events are NOT mutually exclusive?
a) Drawing a queen and drawing a jack from 52 playing cards
b) Drawing a red card and drawing a black card from 52 playing cards
c) Drawing a vowel and drawing a consonant from cards representing the 26 letters of the alphabet
d) Obtaining a total of 8 and rolling doubles (when rolling two dice)
D. This can occur simultaneously (rolling double 4's which = 8) therefore it is not mutually exclusive.
Which of these is not an example of conditional probability?
a) If a student receives a B+ or better in their first Maths test, then the chance of them receiving a B+ or better in their second Maths test is 75%.
b) A group of students were asked to nominate their favourite foods. The probability they like spaghetti and lasagne was 90%.
c) Given that a red marble was picked out of the bag with the first pick, the probability of a blue marble being picked out with the second pick is 0.35.
d) Knowing that the favourite food of a student is hot chips, the probability of their favourite condiment being tomato sauce is 68%.
b.
a) contains the word "then" implying their second grade is conditional on the first.
c) "given"
d) "knowing that"
A coin is biased so that the chance of it falling as a Head when flipped is 0.75. What is the probability of getting 1 heads and 2 tails, when the order does not matter.
P(1H and 2T)
= P(HTT) + P(TTH) + P(THT)
= P(0.75x0.252) + P(0.252x0.75) + (0.25x0.75x0.25)
= 3 x 0.047
= 0.141
Using the apples and bananas Venn Diagram, explain what determining the probability of those who like bananas VS those who like bananas given they like apples would be a different result.
The answer for part a determines the proportion of students who like bananas out of the whole group of students. The part b answer gives the proportion of students who like bananas out of those who like apples.
Using the Spaghetti and Lasagne Venn diagram, what is the probability that a randomly selected student likes lasagne given that they also like spaghetti?
P(L|S) = P(SNL)/P(S)
= 9/40 / 1/2
= 9/20