Assume that on a week day one telephone number out of every ten being called is busy.If 6 randomly selected numbers are called what is the probability that at least three of them will be busy?
use binomial distribution.
I have to go clean seagull poop and snow off high school sailing floats, will check back this afternoon to see if you got it.
looks like Damon is still cleaning seagull poop ....
prob(busy) = 1/10
prob(not busy) = 9/10
prob(at least 3 of 6 are busy)
= C(6,3)(1/10)^3 (9/10^3) + C(6,4) (1/10)^4 (9/10)^2 + ... + C(6,6) (1/10)^6
I will let you do the button-pushing
Thank you Reiny. Indeed we had quite a time getting ready for the first day of sailing practice.
To calculate the probability that at least three out of six randomly selected numbers will be busy, we can use the concept of binomial probability.
Let's break down the problem step by step:
Step 1: Determine the probability of a single telephone number being busy on a weekday. In this case, the probability is given as 1 out of every 10 numbers, or 1/10.
Step 2: Calculate the probability of a single telephone number not being busy on a weekday. Since there is a 1/10 chance of a number being busy, there is a 9/10 chance of a number not being busy.
Step 3: Determine the number of ways we can choose at least three busy numbers out of six selected numbers. We can calculate this using combinations. The number of combinations for choosing at least three busy numbers out of six is:
C(6, 3) + C(6, 4) + C(6, 5) + C(6, 6) = 20 + 15 + 6 + 1 = 42
Step 4: Calculate the probability of getting exactly three busy numbers. This can be calculated using the binomial probability formula:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)
In our case, n = 6 (total number of selected numbers), k = 3 (number of busy numbers), and p = 1/10 (probability of a number being busy):
P(X = 3) = C(6, 3) * (1/10)^3 * (9/10)^(6 - 3)
Step 5: Calculate the probability of getting exactly four, five, or six busy numbers using the same formula as in step 4. In each case, substitute the respective values of k into the formula and calculate the probability.
Step 6: Add up the probabilities of all the cases found in steps 4 and 5. This will give the probability of getting at least three busy numbers out of the six selected.
P(at least three busy numbers) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)
Finally, you can calculate the probability using these steps and substitute the values into the formula to find the final result.