venn diagrams + set notation etc ( chapter 2) (A level book )

Question 1

A and B are independent

Answer 1

A U B = P(A) * P(B)

NOTE: independent probabilities DO NOT HAVE TO ADD TO 1

Question 2

de morgans law

Answer 2

(A n B)’ = A’ U B’

Question 3

Harder question that caught me out !

Question 4

note

Answer 4

first find the intersection probabilities by multiply each event together, and then take these intersection probabilites away from the whole probability

eg if prob of B is said to be 0.5 and C is 0.7 and they are independent, then B n C is 0.5 *0.7

now take it away from each

0.7 - (0.5*0.7 ) , 0.5 - (0.7 * 0.5)

Question 5

“O” with a dash in it

Answer 5

emptty set

Question 6

another note

Answer 6

take probabilities away from venn diagrams in order of priority- eg take all probabilities away from the centre (if its 3 circles) and then take take all probabilites away form each individual intersection

Question 7

NOTE:

Answer 7

DO NOT

forget the area outside of the venn diagram

AND

when it asks for an “and probability” include EVERYTHING that is meant to be added on

Question 8

probability of A U B ?

Answer 8

P(A) + P(B) - P (A n B)

Question 10

p( A’ n B’)

Answer 10

1 - (all the probabilites in the diagram )

Question 11

conditional probability for idnependent events

Answer 11

p (A/B)= P (A/B’)

P(B/A)=P(B/A’)=P(B)

Solve problems using a restricted sample space

Question 12

Question 13

another important note

p( A’)

Answer 13

Make sure to include the probabilities OTUSIDE the box aswell

Question 14

interms of conditional probability, how do you know if something is statistically independent?

Answer 14

if P (A/B)= A

Question 15

find the probability of B/C

( probability of B occuring given that C has to occur first)

Answer 15

1/ 9

Question 18

Answer 18

Question 19

A/ B’

Answer 19

given that B does not occur ,find the probability that A ocurs

A (without the intersection )/ A + (B doesnt occur) + outside value

https://www.youtube.com/watch?v=EzYTgntOZsI&list=PLIy0I0VLj3aiBiiKqyP1bSXjk18R5SAlX&index=9

0:39

Question 20

Note

Answer 20

to get the probabilites of the intersections: multiply the ORIGINAL probabilities together !

Question 21

watch this to get an idea of how to do the notation A/B’

etc… and how to draw venn diagrams whilst substracting the right probabilities

Answer 21

https://www.youtube.com/watch?v=JzTLWX6W6Yc&list=PLIy0I0VLj3aiBiiKqyP1bSXjk18R5SAlX&index=10

Question 22

how to work out the probability of A n B when given A’ n B’ (value outside of the box)

Answer 22

if you dont know the probability of A n B

and you are given P(A) and P(B)

work out P (A U B) –> 1 - p (A’ n B’ (the value outside the box ) )

use p (A n B ) = P(A) + P (B)

Question 24

Answer 24

https://www.youtube.com/watch?v=TTMv_FWDtrI&list=PLIy0I0VLj3aiBiiKqyP1bSXjk18R5SAlX&index=12

( esepecially watch the bit on porbability of kayley losing and john winning

Question 25

Answer 25

dont forget to include ALL of the probabilities

(add the top one to the bottom one to ensure that you have ALL of them )

Question 26

6c

Answer 26

https: //www.youtube.com/watch?v=ZPHhjRRL2SY&list=PLIy0I0VLj3aguQ_C2YTR-ZiSpGl0Xk6cu&index=11
1: 44

Question 27

look at 7b ii

( take note of all the probabilities )

Question 28

“comment on the effectiveness of this drug test ?

Answer 28

- state the probabitiy of false positives etc..

state the obvious: “ From the data in the question, the test fails to find 10% of the people with the condition (since it has a 0.1 chance of producing a negative result when a person has the condition)”

conclusion :

This means that if the test was used on the entire population, 10% of the people with the condition would not be identified and over one third of the people with a positive result would actually not have the condition.

i have now commented on the effectiveness

Question 29

Answer 29

look at “c”

(chances of being late by bus or car/ chances of being late as awhole (do not add the probability of being late by bus or car)