<< Chapter < Page Chapter >> Page >

Construct a probability model for tossing a fair coin.

Outcome Probability
Roll of 1
Roll of 2
Roll of 3
Roll of 4
Roll of 5
Roll of 6
Got questions? Get instant answers now!

Computing probabilities of equally likely outcomes

Let S be a sample space for an experiment. When investigating probability, an event is any subset of S . When the outcomes of an experiment are all equally likely, we can find the probability of an event by dividing the number of outcomes in the event by the total number of outcomes in S . Suppose a number cube is rolled, and we are interested in finding the probability of the event “rolling a number less than or equal to 4.” There are 4 possible outcomes in the event and 6 possible outcomes in S , so the probability of the event is 4 6 = 2 3 .

Computing the probability of an event with equally likely outcomes

The probability of an event E in an experiment with sample space S with equally likely outcomes is given by

P ( E ) = number of elements in  E number of elements in  S = n ( E ) n ( S )

E is a subset of S , so it is always true that 0 P ( E ) 1.

Computing the probability of an event with equally likely outcomes

A number cube is rolled. Find the probability of rolling an odd number.

The event “rolling an odd number” contains three outcomes. There are 6 equally likely outcomes in the sample space. Divide to find the probability of the event.

P ( E ) = 3 6 = 1 2
Got questions? Get instant answers now!
Got questions? Get instant answers now!

A number cube is rolled. Find the probability of rolling a number greater than 2.

2 3

Got questions? Get instant answers now!

Computing the probability of the union of two events

We are often interested in finding the probability that one of multiple events occurs. Suppose we are playing a card game, and we will win if the next card drawn is either a heart or a king. We would be interested in finding the probability of the next card being a heart or a king. The union of two events     E  and  F , written  E F , is the event that occurs if either or both events occur.

P ( E F ) = P ( E ) + P ( F ) P ( E F )

Suppose the spinner in [link] is spun. We want to find the probability of spinning orange or spinning a b .

A pie chart with six pieces with two a's colored orange, one b colored orange and another b colored red, one d colored blue, and one c colored green.

There are a total of 6 sections, and 3 of them are orange. So the probability of spinning orange is 3 6 = 1 2 . There are a total of 6 sections, and 2 of them have a b . So the probability of spinning a b is 2 6 = 1 3 . If we added these two probabilities, we would be counting the sector that is both orange and a b twice. To find the probability of spinning an orange or a b , we need to subtract the probability that the sector is both orange and has a b .

1 2 + 1 3 1 6 = 2 3

The probability of spinning orange or a b is 2 3 .

Probability of the union of two events

The probability of the union of two events E and F (written E F ) equals the sum of the probability of E and the probability of F minus the probability of E and F occurring together ( which is called the intersection of E and F and is written as E F ).

P ( E F ) = P ( E ) + P ( F ) P ( E F )

Computing the probability of the union of two events

A card is drawn from a standard deck. Find the probability of drawing a heart or a 7.

A standard deck contains an equal number of hearts, diamonds, clubs, and spades. So the probability of drawing a heart is 1 4 . There are four 7s in a standard deck, and there are a total of 52 cards. So the probability of drawing a 7 is 1 13 .

The only card in the deck that is both a heart and a 7 is the 7 of hearts, so the probability of drawing both a heart and a 7 is 1 52 . Substitute P ( H ) = 1 4 ,   P ( 7 ) = 1 13 ,   and   P ( H 7 ) = 1 52 into the formula.

P ( E F ) = P ( E ) + P ( F ) P ( E F )                 = 1 4 + 1 13 1 52                 = 4 13

The probability of drawing a heart or a 7 is 4 13 .

Got questions? Get instant answers now!
Got questions? Get instant answers now!

Questions & Answers

stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
v=lbh calculate the volume if i.l=5cm, b=2cm ,h=3cm
Haidar Reply
Need help with math
Peya
can you help me on this topic of Geometry if l help you
litshani
( cosec Q _ cot Q ) whole spuare = 1_cosQ / 1+cosQ
Aarav Reply
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?
Maxwell Reply
the indicated sum of a sequence is known as
Arku Reply
how do I attempted a trig number as a starter
Tumwe Reply
Practice Key Terms 9

Get the best Algebra and trigonometry course in your pocket!





Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Algebra and trigonometry' conversation and receive update notifications?

Ask