A spinner is divided into 10 equal parts and numbered from 1 through 10. What is the probability of spinning a number less than 8 on the first spin and greater than 5 on the second spin?
Numbers less than 8 are 1, 2, 3 , 4, 5, 6, 7
a total of 7 numbers
Each number has a probability of 1 / 10
So the probability of spinning number less than 8 is
7 ∙ 1 / 10 = 7 / 10 = 70 %
Numbers less greater then 5 are 6, 7 , 8 , 9 , 10
a total of 5 numbers
Each number has a probability of 1 / 10
So the probability of spinning number greater then 5 is
5 ∙ 1 / 10 = 5 / 10 = 50%
If the spinner is spun twice the probability that first spinning the number is less than 8 and then spinning the number greater than 5 is the product of these probabilities.
7 / 10 ∙ 5 / 10 = 35 / 100 = 35%
To find the probability of spinning a number less than 8 on the first spin and greater than 5 on the second spin, we need to determine the number of favorable outcomes and the total number of possible outcomes.
Number of favorable outcomes:
Since we want a number less than 8 on the first spin, there are 7 favorable outcomes (1, 2, 3, 4, 5, 6, 7).
On the second spin, we want a number greater than 5. There are 4 favorable outcomes (6, 7, 8, 9, 10).
Total number of possible outcomes:
Since the spinner is divided into 10 equal parts, there are a total of 10 possible outcomes.
Now, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = (7 * 4) / (10 * 10)
Probability = 28 / 100
Probability = 0.28
Therefore, the probability of spinning a number less than 8 on the first spin and greater than 5 on the second spin is 0.28 or 28%.
To find the probability of spinning a number less than 8 on the first spin and greater than 5 on the second spin, we first need to determine the number of favorable outcomes and the total number of possible outcomes.
The spinner is divided into 10 equal parts, numbered from 1 through 10. Since we want to spin a number less than 8 on the first spin, there are 7 favorable outcomes (1, 2, 3, 4, 5, 6, and 7).
For the second spin, we want to spin a number greater than 5. There are 5 favorable outcomes (6, 7, 8, 9, and 10) out of the 10 possible outcomes.
Now let's calculate the probability.
The probability of an event is given by:
Probability = Number of favorable outcomes / Total number of possible outcomes
For the first spin, the probability of spinning a number less than 8 is:
Probability of first spin < 8 = Number of favorable outcomes (7) / Total number of possible outcomes (10)
Probability of first spin < 8 = 7/10
For the second spin, the probability of spinning a number greater than 5 is:
Probability of second spin > 5 = Number of favorable outcomes (5) / Total number of possible outcomes (10)
Probability of second spin > 5 = 5/10
To find the probability of both events occurring, we multiply the probabilities together:
Probability = Probability of first spin < 8 × Probability of second spin > 5
Probability = (7/10) × (5/10) = 35/100 = 0.35
Therefore, the probability of spinning a number less than 8 on the first spin and greater than 5 on the second spin is 0.35 or 35%.