Question

use the data in the following table, which lists drive - thru order accuracy at popular fast food chains. assume that orders are randomly selected from those included in the table.

drive - thru restaurant

	a	b	c	d
order not accurate	34	60	33	13

if one order is selected, find the probability of getting an order from restaurant a or an order that is accurate. are the events of selecting an order from restaurant a and selecting an accurate order disjoint events?

the probability of getting an order from restaurant a or an order that is accurate is
(round to three decimal places as needed.)

Explanation:

Step1: Calculate total number of orders

Total number of orders = \(331 + 280+243 + 142+34 + 60+33 + 13\)
\(=1136\)

Step2: Calculate number of orders from Restaurant A

Number of orders from Restaurant A = \(331 + 34=365\)

Step3: Calculate number of accurate orders

Number of accurate orders = \(331+280 + 243+142\)
\(=996\)

Step4: Calculate number of orders from Restaurant A and accurate

Number of orders from Restaurant A and accurate = \(331\)

Step5: Use the addition - rule for probability

\(P(A\ or\ B)=P(A)+P(B)-P(A\ and\ B)\)
\(P(\text{Restaurant A or Accurate})=\frac{365}{1136}+\frac{996}{1136}-\frac{331}{1136}\)
\(=\frac{365 + 996-331}{1136}=\frac{1030}{1136}\approx0.907\)

Step6: Determine if events are disjoint

Two events are disjoint if they cannot occur at the same time. Since there are orders that are from Restaurant A and are accurate (331 such orders), the events of selecting an order from Restaurant A and selecting an accurate order are not disjoint.

Answer:

\(0.907\); The events are not disjoint.