Question

probability of simple events
the probability of an event describes the likelihood that the event
will happen. it is the ratio of the favorable outcomes to the total
number of possible outcomes.
p(event) = \frac{number of favorable outcomes}{total number of possible outcomes}
kento spins the pointer on the spinner.
find the probability that the pointer lands on 3

1. a favorable outcome is landing on 3. there is

section with 3.

1. there are eight sections on the spinner, so there are

possible outcomes for where the pointer lands.

1. p(3) = \frac{\square}{\square} or 12.5%

find the probability that it lands on a letter
a favorable outcome is landing on a letter. there are
sections with letters.

1. there are eight sections on the spinner, so there are

possible outcomes for where the pointer lands.

1. p(letter) = \frac{\square}{\square} or

find the probability that it lands on 2 or 8

1. a favorable outcome is landing on 2 or 8. there is

section with a 2 and
section with a 8. there are
favorable outcomes.

1. there are eight sections on the spinner, so there are

possible outcomes for where the pointer lands.

1. p(2 or 8) = \frac{\square}{\square} or

Explanation:

Step1: Determine the number of favorable outcomes for landing on 3

From the spinner, there is \(1\) section with \(3\).

Step2: Determine the total number of possible outcomes

There are \(8\) sections on the spinner, so there are \(8\) possible outcomes.

Step3: Calculate \(P(3)\)

Using the formula \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\), we have \(P(3)=\frac{1}{8}\).

Step4: Determine the number of favorable outcomes for landing on a letter

From the spinner, there are \(3\) sections with letters (\(A\), \(B\), \(C\)).

Step5: Calculate \(P(\text{letter})\)

Using the formula \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\), we have \(P(\text{letter})=\frac{3}{8}= 0.375 = 37.5\%\).

Step6: Determine the number of favorable outcomes for landing on 2 or 8

From the spinner, there is \(1\) section with \(2\) and \(1\) section with \(8\). So the number of favorable outcomes for landing on 2 or 8 is \(1 + 1=2\).

Step7: Calculate \(P(2\text{ or }8)\)

Using the formula \(P(\text{event})=\frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\), we have \(P(2\text{ or }8)=\frac{2}{8}=\frac{1}{4}=0.25 = 25\%\).

Answer:

1. \(1\)
2. \(8\)
3. \(\frac{1}{8}\)
4. \(3\)
5. \(8\)
6. \(\frac{3}{8}\), \(37.5\)
7. \(1\), \(1\), \(2\)
8. \(8\)
9. \(\frac{2}{8}\) (or \(\frac{1}{4}\)), \(25\)