Probability The Fundamental Counting Principle Lesson 23 The

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.

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) = s t Number of successful outcomes = 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 S T

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? 35 40 41 68 41 57 62 71 54 68 28 44 62 69 58

Strategy: There is a total of 15 possible outcomes: 35, 28, 40, 44, 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” ?