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	30	56	33	19

if one order is selected, find the probability of getting an order that is not accurate or is from restaurant c. are the events of selecting an order that is not accurate and selecting an order from restaurant c disjoint events?
the probability of getting an order from restaurant c or an order that is not accurate is 0.341. (round to three decimal places as needed.)
are the events of selecting an order from restaurant c and selecting an inaccurate order disjoint events?
the events are not disjoint because it is not possible to pick an accurate order.

Explanation:

Step1: Calculate total number of orders

Total orders = $(335 + 261+247 + 147)+(30 + 56+33 + 19)=1128$

Step2: Calculate number of non - accurate orders

Non - accurate orders = $30 + 56+33 + 19 = 138$

Step3: Calculate number of orders from Restaurant C

Orders from Restaurant C = $247+33 = 280$

Step4: Calculate number of non - accurate orders from Restaurant C

Non - accurate orders from Restaurant C = 33

Step5: Use the addition rule for probability

$P(\text{not accurate or from C})=P(\text{not accurate})+P(\text{from C})-P(\text{not accurate and from C})$
$P(\text{not accurate})=\frac{138}{1128}$, $P(\text{from C})=\frac{280}{1128}$, $P(\text{not accurate and from C})=\frac{33}{1128}$
$P(\text{not accurate or from C})=\frac{138 + 280-33}{1128}=\frac{385}{1128}\approx0.341$

Step6: Determine if events are disjoint

Disjoint events cannot occur at the same time. Since there are non - accurate orders from Restaurant C (33 non - accurate orders from C), it is possible for an order to be non - accurate and from Restaurant C. So the events are not disjoint.

Answer:

The probability of getting an order that is not accurate or is from Restaurant C is approximately $0.341$. The events of selecting an order that is not accurate and selecting an order from Restaurant C are not disjoint.