At Guadalajara Airport, passengers must claim their luggage and then proceed to Customs. In the Customs area, each passenger will press a button that activates a modified stoplight. This light has only red and green bulbs. If the green light shows, the passenger is free to go. If the light turns red, then Customs agents will inspect the passenger's luggage. Customs officials cliam that the light has probability 0.30 of showing red on any press of the button. You are traveling with 6 family members, and you are the seventh person in line.

Find the probability that exactly one of the family memebers in front of you is stopped.

probability of exactly one out of six.

Binomial distribution
P(x=1) = C(6,1) (.3)^1 (.7)^5
.3^1 = .3
.7^5 = .168
C(6,1) = 6!/[ 1! (5!) ] = 6
so 6 * .3 * .168 = .302

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Thanks for da answers

To solve this problem, we can use the concept of binomial probability. Let's break it down into steps:

Step 1: Define the variables:
Let X be the number of family members in front of you who get stopped.
The probability of a family member getting stopped is p = 0.30.

Step 2: Calculate the probability of exactly one family member being stopped:
Using the binomial probability formula, the probability of exactly one family member being stopped can be calculated as:
P(X = 1) = (nCx) * p^x * (1-p)^(n-x)

Here, n = 6 (total family members) and x = 1 (one family member stopped).

P(X = 1) = (6C1) * 0.30^1 * (1 - 0.30)^(6 - 1)
= (6C1) * 0.30 * 0.70^5

The notation "6C1" represents the combination formula to select 1 family member out of 6, which is calculated as 6! / (1! * (6-1)!), resulting in 6.

P(X = 1) = 6 * 0.30 * 0.70^5

Step 3: Calculate the probability of you being the seventh person in line with exactly one family member stopped:
Since you are the seventh person in line, all family members in front of you need to be not stopped (green light) except for exactly one.

P(you being seventh, one family member stopped) = (1 - 0.30)^6 * P(X = 1)

P(you being seventh, one family member stopped) = 0.70^6 * (6 * 0.30 * 0.70^5)

Finally, compute this value to find the probability.