Bike Riders and Helmet Probability
What is the probability that at least one of the four randomly chosen bike riders does not wear a helmet all the time, given that 77% of bike riders sometimes ride without a helmet?
Probability Calculation
To find the probability that at least one of the four randomly chosen bike riders does not wear a helmet all the time, we can calculate the complement of the probability that all four riders wear a helmet all the time.
Given that 77% of bike riders sometimes ride without a helmet, the probability that a randomly chosen rider wears a helmet all the time is 1 - 0.77 = 0.23.
The probability that all four riders wear a helmet all the time is 0.23⁴, as we assume the events are independent.
The probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we calculate the probability that all four riders wear a helmet all the time and subtract it from 1 to find the probability that at least one of them does not wear a helmet all the time.
By using the complement rule, we can simplify the calculation by finding the probability that none of the riders wears a helmet all the time (0.23⁴) and subtract it from 1.
This approach allows us to determine the desired probability based on the given information about the percentage of bike riders who sometimes ride without a helmet.
The probability that at least one of the four randomly chosen bike riders does not wear a helmet all the time can be calculated using the complement rule. Since 77% of bike riders sometimes ride without a helmet, this means the probability of a rider wearing a helmet all the time is 1 - 0.77 = 0.23.
To find the probability of all four riders wearing a helmet all the time, we raise the probability of a single rider wearing a helmet (0.23) to the power of 4, as these events are assumed to be independent.
The complement rule states that the probability of at least one of the events happening is equal to 1 minus the probability of none of the events happening. Therefore, by subtracting the probability of all four riders wearing helmets all the time from 1, we can find the probability of at least one rider not wearing a helmet all the time.
Using this method, we can determine the likelihood of having at least one rider not wearing a helmet among the four randomly chosen bike riders. This calculation provides insights into the overall safety measures taken by bike riders and the importance of helmet usage.