Scribd
Upload
167 views

Probability of Independent Events

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Some other examples of independent events are: Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die.

Uploaded by

Yash Keith Smith
Copyright
© © All Rights Reserved
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
167 views

Probability of Independent Events

Two events, A and B, are independent if the fact that A occurs does not affect the probability of B occurring. Some other examples of independent events are: Landing on heads after tossing a coin AND rolling a 5 on a single 6-sided die.

Uploaded by

Yash Keith Smith
Copyright
© © All Rights Reserved
Available Formats
Download as PPTX, PDF, TXT or read online on Scribd
You are on page 1/ 10

PROBABILITY

PROBABILITY
OF
OF
INDEPENDENT
INDEPENDENT
EVENTS
EVENTS

PROBABILITY

PROBABILITY IS THE BRANCH OF MATHEMATICS THAT


DEALS WITH THE STUDY CHANCE. PROBABILITY DEALS
WITH THE STUDY OF EXPERIMENTS AND THEIR
OUTCOMES.
PROBABILITY KEY TERMS
EXPERIMENT

AN EXPERIMENT IN PROBABILITY IS A TEST TO


SEE WHAT WILL HAPPEN INCASE YOU DO SOMETHING. A
SIMPLE EXAMPLE IS FLIPPING A COIN. WHEN YOU FLIP A
COIN, YOU ARE PERFORMING AN EXPERIMENT TO SEE
WHAT SIDE OF THE COIN YOU'LL END UP WITH.

OUTCOME
AN OUTCOME IN PROBABILITY REFERS TO A SINGLE (ONE)
RESULT OF AN EXPERIMENT. IN THE EXAMPLE OF AN EXPERIMENT
ABOVE, ONE OUTCOME WOULD BE HEADS AND THE OTHER WOULD
BE TAILS.

EVENT
AN EVENT IN PROBABILITY IS THE SET OF A GROUP OF
DIFFERENT OUTCOMES OF AN EXPERIMENT. SUPPOSE YOU FLIP A
COIN MULTIPLE TIMES, AN EXAMPLE OF AN EVENT WOULD THE
GETTING A CERTAIN NUMBER OF HEADS.

SAMPLE SPACE
A SAMPLE SPACE IN PROBABILITY IS THE TOTAL NUMBER OF ALL THE
DIFFERENT POSSIBLE OUTCOMES OF A GIVEN EXPERIMENT. IF YOU FLIPPED
A COIN ONCE, THE SAMPLE SPACE S WOULD BE GIVEN BY:

S = {HEAD, TAIL}
IF YOU FLIPPED THE COIN MULTIPLE TIMES, ALL THE DIFFERENT
COMBINATIONS OF HEADS AND TAILS WOULD MAKE UP THE SAMPLE SPACE.
A SAMPLE SPACE IS ALSO DEFINED AS A UNIVERSAL SET FOR THE
OUTCOMES OF A GIVEN EXPERIMENT.

INDEPENDENT EVENTS
WHEN TWO EVENTS ARE SAID TO BE INDEPENDENT OF EACH
OTHER, WHAT THIS MEANS IS THAT THE PROBABILITY THAT ONE
EVENT OCCURS IN NO WAY AFFECTS THE PROBABILITY OF THE OTHER
EVENT OCCURRING. AN EXAMPLE OF TWO INDEPENDENT EVENTS IS
AS FOLLOWS; SAY YOU ROLLED A DIE AND FLIPPED A COIN. THE
PROBABILITY OF GETTING ANY NUMBER FACE ON THE DIE IN NO WAY
INFLUENCES THE PROBABILITY OF GETTING A HEAD OR A TAIL ON
THE COIN.
DEPENDENT EVENTS
WHEN TWO EVENTS ARE SAID TO BE DEPENDENT, THE PROBABILITY
OF ONE EVENT OCCURRING INFLUENCES THE LIKELIHOOD OF THE
OTHER EVENT.

A CARD IS CHOSEN AT RANDOM FROM A DECK OF 52 CARDS. IT IS


THEN REPLACED AND A SECOND CARD IS CHOSEN. WHAT IS THE
PROBABILITY OF CHOOSING A JACK AND THEN AN EIGHT?
P(JACK) =
P(8)

4/25
=

P(JACK AND 8)

4/52
= P(JACK) P(8)
= 4/52

4/52

=16/2704
= 1/169

A jar contains 3 red, 5 green, 2 blue and 6 yellow marbles.


A marble is chosen at random from the jar. After replacing
it, a second marble is chosen. What is the probability of
choosing a green and then a yellow marble?
P(green)

5 /16

P(yellow)

6 /16

P(green and yellow) = P(green) P(yellow)


= 5 /16 6 /16
=
30 /256
=
15 /128

A COIN IS TOSSED AND A SINGLE 6-SIDED DIE IS ROLLED. FIND


THE PROBABILITY OF LANDING ON THE HEAD SIDE OF THE
COIN AND ROLLING A 3 ON THE DIE.

P(HEAD) =
P(3) =

1/6

P(HEAD AND 3) =

P(HEAD) P(3)
=
=

1/2

1/6
1 /12

You might also like