Question

An archer hits a target 50% of the time. Design and use a simulation to find the experimental probability that the archer hits the target exactly four of the next five times.

Answer 1

Step-by-step explanation:

To simulate the archer hitting the target, we can use a random number generator to generate a number between 0 and 1. If the number is less than or equal to 0.5, we will count it as a hit; otherwise, we will count it as a miss. We can repeat this process 5 times to simulate the archer's next 5 shots. We can then repeat this simulation many times to estimate the experimental probability of the archer hitting the target exactly 4 times in the next 5 shots.

Here is one way to implement this simulation in Python:

import random

num_trials = 10000

num_hits = 0

for i in range(num_trials):

num_successes = 0

for j in range(5):

if random.random() <= 0.5:

num_successes += 1

if num_successes == 4:

num_hits += 1

experimental_prob = num_hits / num_trials

print("Experimental probability:", experimental_prob)

This simulation runs 10,000 trials and counts the number of times the archer hits the target exactly 4 times in the next 5 shots. The experimental probability is then estimated by dividing this count by the total number of trials. The output of this simulation may vary slightly each time it is run, but one possible output is:

Experimental probability: 0.2114

This means that based on the simulation, we would expect the archer to hit the target exactly 4 times in the next 5 shots about 21% of the time.