Download Lesson 6: Independent Events

Starter
In each experiment, determine whether the events A
and B are mutually exclusive.
The numbers 5 – 10 are written on identical pieces of
card and placed in a bag. A card is selected at
random from the bag. Let A be the event ‘a square is
chosen’ and B be the event ‘an even number is chosen’
Mutually exclusive – NO intersection
The numbers 2 – 9 are written on identical pieces of
card and placed in a bag. A card is selected at
random from the bag. Let A be the event ‘an even
number is chosen’ and B be the event ‘a multiple of
three is chosen’
Not mutually exclusive – intersection of sets is number 6
Note 8: Independent Events
When the occurrence of A has no effect on the
likelihood of B occurring, the two events are
independent.
Examples: Are the following independent or not?
Events A = {person has red hair) and B = {person passes
Independent
Statistics exam)
Events A = {person has done all revision supplied} and B
= {person passes Statistics exam} Not Independent
The statistical definition of independent events is:
P(A ∩ B) = P(A) x P(B)
Example: The probability an individual has blonde hair
is 0.5 and the probability an individual has blue eyes is
0.3. The probability that an individual has blonde hair
and blue eyes is 0.21.
Explain whether blonde hair and blue eyes are
independent events.
(BH ∩ BE) = 0.21
(BH) x P(BE) = 0.5 x 0.3 = 0.15
0.21 ≠ 0.15
Therefore, the events are not independent.
Page 163
Exercise E