A spinner numbered 1 to 50 is spun twice. Find the probability that the total from the two spins is:
a. 51
b.55
To find the probability that the total from the two spins is a specific number, we need to count the number of favorable outcomes (combinations of two numbers that sum up to the desired total) and divide it by the total number of possible outcomes.
a) To find the probability that the total from the two spins is 51, we need to find the number of combinations that add up to 51.
We can start by listing all the possible pairs of numbers that add up to 51:
(1, 50), (2, 49), (3, 48), ..., (48, 3), (49, 2), (50, 1)
There are a total of 2 combinations that add up to 51: (1, 50) and (50, 1).
Since there are 50 numbers on the spinner and we are spinning it twice, the total number of possible outcomes is 50 * 50 = 2500.
Therefore, the probability that the total from the two spins is 51 is 2/2500, which can be simplified to 1/1250.
b) To find the probability that the total from the two spins is 55, we need to find the number of combinations that add up to 55.
We can start by listing all the possible pairs of numbers that add up to 55:
(5, 50), (6, 49), (7, 48), ..., (46, 9), (47, 8), (48, 7), (49, 6), (50, 5)
There are a total of 10 combinations that add up to 55.
Since there are 50 numbers on the spinner and we are spinning it twice, the total number of possible outcomes is 50 * 50 = 2500.
Therefore, the probability that the total from the two spins is 55 is 10/2500, which can be simplified to 1/250.
To find the probability of getting a particular total from two spins of a spinner numbered 1 to 50, we need to determine the number of favorable outcomes and divide it by the total number of possible outcomes.
a. To find the probability that the total from the two spins is 51, we need to determine the number of ways we can get a sum of 51.
First, let's consider the possible outcomes of the first spin. The spinner is numbered from 1 to 50, so there are 50 possible outcomes for the first spin.
Now, let's consider the possible outcomes of the second spin. Again, there are 50 possible outcomes for the second spin.
To get a total of 51, we need to find the number of pairs of outcomes where the sum is 51. There is only one such pair: (1, 50).
Therefore, the number of favorable outcomes is 1.
The total number of possible outcomes is the product of the possible outcomes for each spin, which is 50 * 50 = 2500.
Now, we can calculate the probability:
Probability of getting a total of 51 = Number of favorable outcomes / Total number of possible outcomes
= 1 / 2500
= 0.0004
Therefore, the probability of getting a total of 51 is 0.0004.
b. To find the probability that the total from the two spins is 55, we follow the same process.
Again, let's consider the possible outcomes of the first spin. There are 50 possible outcomes.
Next, let's consider the possible outcomes of the second spin. There are 50 possible outcomes.
To get a total of 55, we need to find the number of pairs of outcomes where the sum is 55. In this case, there are no pairs of outcomes that sum up to 55.
Therefore, the number of favorable outcomes is 0.
The total number of possible outcomes is still 50 * 50 = 2500.
Now, we can calculate the probability:
Probability of getting a total of 55 = Number of favorable outcomes / Total number of possible outcomes
= 0 / 2500
= 0
Therefore, the probability of getting a total of 55 is 0.
51
= 1+50
= 2 + 49
...
= 50+1
there are 50 such cases out of 50(50)
so prob = 50/(50*50) = 1/50
55 , the smallest we can start with is 5
55
= 5 + 50
= 6 + 49
..
= 50 + 5 ----> 46 of them
prob = 46/2500 = 23/1250