A. The probability that you ask at least 8 people before you find someone with a job means that the first 7 people you asked did not have a job. The probability that one person does not have a job is 1 - 0.65 = 0.35. So, to find the probability that the first 7 people you asked did not have a job, you multiply the probabilities: (0.35)^7 = 0.052697. However, this is the probability of asking 7 people, you must also multiply by the probability of finding a job on the 8th try, 0.65: 0.052697 * 0.65 = 0.034253. So the probability is 3.43%.
B. You ask at most 4 people before you find someone with a job, so this means the probability could be on the 1st, 2nd, 3rd, or 4th try. We can calculate each separately and then add them together to find the total probability.
- Finding a job on the 1st try: 0.65
- Finding a job on the 2nd try: (0.35) * (0.65) = 0.2275
- Finding a job on the 3rd try: (0.35)^2 * (0.65) = 0.079625
- Finding a job on the 4th try: (0.35)^3 * (0.65) = 0.02796875
So, the total probability of finding a job within the first 4 tries is 0.65 + 0.2275 + 0.079625 + 0.02796875 = 0.98509375. So the probability is about 98.51%.
C. To find the probability between 15 and 29 people in a group of 50 have a job, we can use the binomial probability formula, which is: P(x) = C(n, x) * (p^x) * [(1-p)^(n-x)], where n is the total number of trials, x is the number of successful trials, p is the probability of success, and C is the combination function.
Summing up the probabilities for all values between 15 and 29: P(15) + P(16) + ... + P(29)
This involves lengthy calculations, so I recommend using a calculator or software to compute the sum. Using a binomial probability calculator, we find the probability to be approximately 0.397. So the probability is about 39.70%.
D. In a group of 50 students, since the probability of not having a job is 35% (0.35), we can multiply that probability by the number of students in the group to find out how many WITHOUT jobs we would expect to see: 50 * 0.35 = 17.5. So, we would expect to see about 17.5 students WITHOUT jobs in a group of 50. Note that the actual number of students has to be a whole number, but 17.5 gives an idea of the average.
The probability that a student in this school has a job is 65%. What is the probability that:
A. You ask at least 8 people before you find someone with a job?
B. You ask at most 4 people before you find someone with a job?
C. Between 15 and 29 people in a group of 50 will have a job?
D. How many students WITHOUT jobs would you expect to see in a group of 50?
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