Question

based on a survey, assume that 53% of consumers are comfortable having drones deliver their purchases. suppose we want to find the probability that when 4 condumers ate randomly selected, exactly 2 of them are comfortable with the drones. what is wrong eith using the multiplication tule to find the probability of getting 2 vonsumers comfortable with drones followed by 2 consumers not comfortable, as in calculation: (0.53)(0.53)(0.47)(0.47)=0.0621?

Answer 1

We cannot apply the multiplication rule to find the probability of getting 2 consumers comfortable with drones followed by 2 consumers not comfortable because any of the two consumers out of 4 can/cannot be comfortable with drones.

Number of ways we have two consumers out of 4 can be comfortable with drones is,

So, the probability of getting 2 consumers comfortable with drones followed by 2 consumers not comfortable is,

6 * (0.53)(0.53)(0.47)(0.47) = 0.3723049

Here X (the number of consumers comfortable with drones) will follow Binomial distribution with parameters n = 4 and p = 0.53.

= 0.3723049