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Probability & The Fundamental Counting Principle - PowerPoint PPT Presentation
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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
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.
Read through the following lesson. Answer the Try This questions. Show your work!
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:
P(E) = =
Number of successful outcomes
s
t
Total number of outcomes
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
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
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
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?
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
- 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
If a computer randomly chooses a letter in the word “algebra,” what is the probability that it chooses the letter “a” ?
