Probability of Receiving Local and Long-Distance Calls at a Communication Tower
Question 1: What is the probability of receiving a long-distance call at the communication tower?
Based on long-range communications, the probability that the tower will receive a local call is 0.75. Of these local calls, 60% are long-distance calls.
Question 2: What is the probability of receiving a local call that is not long-distance?
Based on the given data, what can we calculate about the probability of receiving different types of calls at the communication tower?
Answer:
Probability theory plays a crucial role in understanding the likelihood of various events occurring, such as receiving different types of calls at a communication tower. In this scenario, we are provided with the probability of receiving a local call and the percentage of long-distance calls within those local calls.
To determine the probability of receiving a long-distance call at the communication tower, we first consider that the probability of receiving a local call is 0.75. From this, we know that 60% of the local calls are long-distance calls. To find the probability of a long-distance call, we multiply the probability of receiving a local call by the percentage of long-distance calls within those local calls:
0.75 * 0.6 = 0.45
Therefore, the probability of receiving a long-distance call is 0.45.
Next, we look at the probability of receiving a local call that is not long-distance. Since 60% of local calls are long-distance, the remaining 40% must be local calls that are not long-distance. To calculate this probability, we subtract the probability of receiving a long-distance call from the probability of receiving a local call:
0.75 - 0.45 = 0.30
Thus, the probability of receiving a local call that is not long-distance is 0.30.
Probability is a fundamental concept that can be applied to real-world scenarios, allowing us to make predictions and informed decisions. By breaking down the problem into smaller parts and using logical reasoning, we can determine the probabilities of different events occurring. In this case, we utilized the information provided about the probability of receiving local calls and the proportion of long-distance calls within those local calls to calculate the probabilities of receiving specific types of calls at the communication tower.