a spinner is divided into 10 sectors. the number 1 through5 are each placed in two different sectors. find the probability of each event.
P(less than 3)
P (5)
p (8)
P is the same as if there were a 5-section wheel with just the numbers 1-5.
To find the probability of each event, we need to determine the total number of favorable outcomes and the total number of possible outcomes.
Given:
- Spinner is divided into 10 sectors
- Numbers 1 to 5 are placed in two different sectors each
Total number of possible outcomes = Total number of sectors = 10
Event 1: P(less than 3)
Favorable outcomes = {1, 2}
Total number of favorable outcomes = 2
P(less than 3) = Total number of favorable outcomes / Total number of possible outcomes
P(less than 3) = 2 / 10
P(less than 3) = 1/5
Therefore, the probability of getting a number less than 3 is 1/5 or 0.2.
Event 2: P(5)
Favorable outcomes = {5}
Total number of favorable outcomes = 1
P(5) = Total number of favorable outcomes / Total number of possible outcomes
P(5) = 1 / 10
P(5) = 1/10
Therefore, the probability of getting a 5 is 1/10 or 0.1.
Event 3: P(8)
Favorable outcomes = {8}
Total number of favorable outcomes = 1
P(8) = Total number of favorable outcomes / Total number of possible outcomes
P(8) = 1 / 10
P(8) = 1/10
Therefore, the probability of getting an 8 is 1/10 or 0.1.
To find the probability of each event, we need to know the total number of possible outcomes and the number of favorable outcomes.
Given that the spinner is divided into 10 equal sectors, we know that there are 10 possible outcomes. Now let's determine the favorable outcomes for each event:
Event 1: P(less than 3)
The numbers less than 3 on the spinner are 1 and 2. Each of these numbers is placed in two different sectors. So, there are a total of 4 favorable outcomes (2 sectors with 1 and 2 each). Therefore, the probability of this event is 4/10 or 2/5.
Event 2: P(5)
The number 5 is placed in two different sectors on the spinner. Hence, there are 2 favorable outcomes. Thus, the probability of this event is 2/10 or 1/5.
Event 3: P(8)
Since the number 8 is not included among the numbers assigned to any sectors of the spinner, there are no favorable outcomes for this event. Therefore, the probability of this event is 0.
To recap:
- P(less than 3) = 2/5
- P(5) = 1/5
- P(8) = 0