A spinner numbered 1 to 50 with equal size sectors is spun twice. Find the probability that the total for
the two spins is:
a 100
b 51
c 99
d 52
e 55
To find the probability of the total for two spins, we need to determine the number of favorable outcomes (the number of ways to get each total) and the total number of possible outcomes (the total number of different combinations).
a) To get a total of 100, we can have the first spin be any number from 1 to 50, and the second spin must be 100 minus the number obtained in the first spin. So, if the first spin is 1, the second spin must be 99. If the first spin is 2, the second spin must be 98, and so on. In this case, there is only one way to get a total of 100 (1 + 99). Therefore, the number of favorable outcomes is 1.
b) To get a total of 51, the numbers obtained in the two spins must sum up to 51. However, since each spin has equal size sectors, it is not possible to get a sum of 51 from two different spins. Therefore, the number of favorable outcomes is 0.
c) To get a total of 99, we can have the first spin be any number from 1 to 49, and the second spin must be 99 minus the number obtained in the first spin. So, if the first spin is 1, the second spin must be 98. If the first spin is 2, the second spin must be 97, and so on. In this case, there are 49 possible outcomes that sum up to 99. Therefore, the number of favorable outcomes is 49.
d) To get a total of 52, there are a few possible combinations. The first spin can be 1 and the second spin can be 51. The first spin can be 2 and the second spin can be 50. Continuing this pattern, we find that there are 48 possible outcomes that sum up to 52. Therefore, the number of favorable outcomes is 48.
e) To get a total of 55, there are a few possible combinations. The first spin can be 5 and the second spin can be 50. The first spin can be 6 and the second spin can be 49. Continuing this pattern, we find that there are 45 possible outcomes that sum up to 55. Therefore, the number of favorable outcomes is 45.
The total number of possible outcomes is fixed at 50 for each spin, so we multiply the number of favorable outcomes by the total number of possible outcomes to find the probability.
a) Probability of getting a total of 100 = (1 favorable outcome) / (50 possible outcomes) = 1/50.
b) Probability of getting a total of 51 = (0 favorable outcomes) / (50 possible outcomes) = 0.
c) Probability of getting a total of 99 = (49 favorable outcomes) / (50 possible outcomes) = 49/50.
d) Probability of getting a total of 52 = (48 favorable outcomes) / (50 possible outcomes) = 48/50 = 24/25.
e) Probability of getting a total of 55 = (45 favorable outcomes) / (50 possible outcomes) = 45/50 = 9/10.
since only 50+50 = 100, the chance is 1/50 * 1/50 = 1/2500
any number can come up first, but only 1 second number will make the sum 51, so prob = 1/50
see what you can do with the others.