Algebra 1 Common Core Student Edition, Grade 8-9

Get t in g Read y!

I want to win

a p riz e. W h a t's

th e best decision?

—.......----, -------

On one game show, you g et one chance t o spin t h e wheel

at t h e r ig h t. I f t h e spinner st op s on a r ed sect io n , you win

a p r i ze o f yo u r ch o i ce. On an o t h er game sho w , you cho o se

one of 15 envelopes. Th r ee o f t h e envelopes cont ain a prize

that you chose. Which game show would you rather be on?

Ex p l a i n y o u r r e a so n i n g.

i M A T H E M A T I C A L

I P R A C T I C E S In th e Solve It, spinning red an d choosing th e right envelope are desired outcom es. An

outcom e is th e result of a single trial, such as spinning a w heel. The sam ple space is all

th e possible outcom es. An event is any outcom e or group of outcom es. The outcom es

th a t m atch a given event are favorable outcom es.

Object ive To find theoretical a n d experim ental probabilities

Theoretical and

Experimental Probability

S-CP.A.1 Describe events as subsets o f a sample space

(the set o f outcomes) using characteristics (or categories)

o f the outcomes, or as... complements of other

events.... Also S-CP.A.4

MP 1, MP 2, MP 3, M P 4, M P 6

Common Core State Standards

Lesso n

Vocabulary

• outcom e


• sample space


• event


• probability


• theoretical
  probability


• com plem ent o f
  an event


• odds


• experim ental
  probability

Here is h ow th ese term s apply to rolling an even n u m b e r o n a n u m b e r cube.

event sample space favorable outcomes

ro llin g an even n u m b e r 1, 2, 3, 4, 5, 6 2, 4 ,6

Esse n t i a l U n d e r st a n d i n g The probability of an event, or P(event), tells you

how likely it is th a t th e event will occur. You can find probabilities by reasoning

m athem atically or by using d ata collected from an experim ent.

In th e n u m b er-cu b e exam ple above, th e outcom es in the sam ple space are equally

likely to occur. W hen all possible outcom es are equally likely, y ou can find the

theoretical probability of a n event using th e following formula.

th eo retical p ro b a b ility P (ev e n t) = number of favorable outcomes

r number of possible outcomes

P (rolling a n even n u m b er) =^3 0 = 21

You can write th e probability of a n event as a fraction, a decim al, or a percent. The

probability of a n event ranges from 0 to 1.

impossiblei

equally likely to occur

or not occur

I

certain

1 1

0 —

1

— less likely 0.5 more likely ■

1

^(P ow erA lgebra.com ^ l|i Lesson 12-7 Theoretical and Experimental Probability 769