a survey from teeneage research unlimited found that 30% of teenage consumers receive their spending money from parttime jobs. If 5 teenagers are selected at random, find the probability that at least 3 of them have part time jobs
For5 =3*3*3*3*3*3
student
You want the probability of 3, 4 or all 5 having part-time jobs.
for 3 = .3*.3*.3*.7*.7 = ?
for 4 = .3*.3*.3*.3*.7 = ?
for 5 = ?
For either-or probabilities, add the individual probabilities.
Well, since we're talking about teenagers and part-time jobs, I'm reminded of my own attempts at working as a teenager. Let's crunch the numbers and see what we get!
First, let's find the probability that exactly 3 teenagers have part-time jobs. Using the binomial probability formula, this would be:
P(3) = C(5, 3) * (0.3)^3 * (0.7)^2
Where C(5, 3) represents the combination of choosing 3 out of 5 teenagers.
Next, let's find the probability that exactly 4 teenagers have part-time jobs. Similar to above, this would be:
P(4) = C(5, 4) * (0.3)^4 * (0.7)^1
Finally, let's find the probability that all 5 teenagers have part-time jobs:
P(5) = C(5, 5) * (0.3)^5 * (0.7)^0
Now, to find the probability that at least 3 teenagers have part-time jobs, we just need to add up the probabilities of these three scenarios:
P(at least 3) = P(3) + P(4) + P(5)
I'll leave it to you to calculate the values and sum them up! Remember, math is fun! Just like juggling chainsaws! Okay, maybe math is slightly safer than that.
To find the probability that at least 3 teenagers out of 5 have part-time jobs, we can use a combination of probability calculations.
Step 1: Calculate the probability that exactly 3, 4, or 5 teenagers have part-time jobs.
The probability of exactly 3 teenagers having part-time jobs can be calculated using the binomial probability formula:
P(X = k) = nCk * p^k * (1 - p)^(n - k)
where:
n is the total number of trials (number of teenagers selected),
k is the number of successful outcomes (number of teenagers with part-time jobs),
p is the probability of success (proportion of teenagers with part-time jobs), and
nCk is the combination of n and k.
In this case, n = 5 (total number of teenagers selected), k = 3 (number of teenagers with part-time jobs), and p = 0.3 (proportion of teenagers with part-time jobs).
P(X = 3) = 5C3 * 0.3^3 * (1 - 0.3)^(5 - 3)
P(X = 3) = 10 * 0.3^3 * 0.7^2
Similarly, calculate P(X = 4) and P(X = 5) using the same formula but with k = 4 and k = 5.
Step 2: Sum up the probabilities from step 1 to calculate the probability of at least 3 teenagers having part-time jobs.
P(at least 3 teenagers with part-time jobs) = P(X = 3) + P(X = 4) + P(X = 5)
By summing up these probabilities, you will get the probability that at least 3 out of 5 randomly selected teenagers have part-time jobs.