Question

Suppose that you and two friends go to a restaurant, which last month filled approximately 88.2% of the orders correctly. Complete parts (a) through (e) below. Click the icon to view the order-filling data for two other restaurants. a. What is the probability that all three orders will be filled correctly? The probability is . (Round to four decimal places as needed.)

Answer 1

The probability that all three orders will be filled correctly, given the restaurant's accuracy rate of 88.2%, is approximately 0.6865 when rounded to four decimal places.

Step-by-step explanation:

The question involves calculating the probability of an event occurring under given conditions. In this case, the event is that all three orders at a restaurant are filled correctly and the condition is that the restaurant's historical accuracy rate is 88.2%.

To find the probability that all three orders will be filled correctly, we use the multiplication rule for independent events.

The probability of one order being correct is 0.882. Since the orders are filled independently, the probability that all three orders are correct is (0.882) × (0.882) × (0.882), which equals approximately 0.6865 when rounded to four decimal places.