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Probability & The Fundamental Counting Principle

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Probability & The Fundamental Counting Principle. Lesson 23. The six faces of a die have dots on them corresponding to the numbers 1 trough 6. 1 dot shows on the top of the die above. If a die is tossed many times, the 1-dot face should appear on top about 1 out of 6 times, or 1/6 if the time.

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Presentation Transcript
slide2
The six faces of a die have dots on them corresponding to the numbers 1 trough 6.
  • 1 dot shows on the top of the die above.
  • If a die is tossed many times, the 1-dot face should appear on top about 1 out of 6 times, or 1/6 if the time.
slide4
We say that the probability of rolling a 1 in one toss is 1/6.
  • In the ratio 1/6,

1 is the number of successful outcomes: s

6 is the total number of possible outcomes: t.

this suggests the following formula for the probability of an event
This suggests the following formula for the probability of an event:

P(E) = =

Number of successful outcomes

s

t

Total number of outcomes

slide6
Example One:

This is a dart board with both shaded and unshaded squares. If you throw a dart without looking and it lands on the board, what is the probability that it landed on a shaded square?

A. 2/5 B. ½ C. 3/5 D. 2/3

slide7
Strategy:
  • There is a total of 20 possible squares or outcomes.
  • 8 squares are shaded: 8 favorable or successful outcomes.

There are 8 favorable outcomes out of 20 possible outcomes.

The chances or probability that the dart will land on a shaded square if therefore 8 out of 20 or 8/20.

8 number of successful outcomes

20 total number of possible outcomes

SOLUTION: the probability is 8/20 = 2/5 choice A

try this 1
Try This # 1

If the spinner below is spun, what is the possibility that the arrow will land on an S?

A. 5/8 B. 3/8 C. 3/5 D. ½

S

P

R

T

S

P

T

S

slide9
Example 2:

The points scored by Middletown Intermediate School are recorded below. What is the probability that the team scored fewer than 54 points in one game chosen random?

slide10
Strategy:

There is a total of 15 possible outcomes:

35, 28, 40, 44, 41, 41 - 6 scores less than 53

SO the probability of scoring less than 54 is :

number of successful outcomes 6

total number of outcomes 15

6/15 = 2/5

try this 2
Try This # 2
  • Use the table of scores in Example 2 to answer the following question.

What is the probability that the team scored greater than 60 points in one game chosen at random?

try this 3
Try This # 3

If a computer randomly chooses a letter in the word “algebra,” what is the probability that it chooses the letter “a” ?