I wonder what I should calculate for the following subtask, but first of all the general task:
On a through road, the proportion of car drivers who use their mobile phones while driving is to be investigated. We assume that drivers make or do not make phone calls independently of each other. The probability of a driver making a phone call is p.
Now to the subtask:
Determine the unknown probability that none of 10 passing cars will be driven by a person on the phone with a probability of 25%.
On
You should first get solid the meaning of what the question is asking for. You are asked to find some probability $p$ of each individual making a call, such that the probability that ten such individuals are all not making a call is $\frac14$.
The probability of each individual not making a call is $(1-p)$ and to get the happy situation of nobody making a call you need ten independent trials in which this $(1-p)$ chance is satisfied. So you will need to look at $(1-p)^{10}$ and compare it to the probability you want, which is $\frac14$.
Just for practice -- what if the phone usage were not independent? What if when driver 1 makes a call, he always calls driver 10, and driver ten is only on the phone if driver $1$ has called her? How would that change your answer?
Please do not work on this problem while driving. That's what your phone is for.
$0.25$ is the chance that none of the drivers is using a phone. What is the chance that the first drive is not using a phone in terms of $p$? The second? All of the first $10$? Now set that equal to $0.25$ and solve for $p$.