Assume that replacement was considered when choosing. Are the events 0.0206 and 0.0205
Detailed explanation:
from the query, considering
Order Accurate = 328 273 242 142
Order Not Accurate = 32 54 37 20
Make the total number of orders a
T.O = 328+273+242+142+32+54+37+20 = 1128.
a) Make the assumption that restaurant D is the source of the initial order.
= Total number of orders / Number of orders from restaurant D
= 162 / 1128 = 0.1436
The second order probability is 0.1436.
This is due to the fact that the selections are made with replacement, which implies that the order is the same, as indicated by the question.
Thus, the likelihood of receiving two orders is equal to 0.1436 * 0.1436, or 0.0206.
Note: There is a 0.0206 percent chance of receiving two orders from restaurant B.
This is so that selecting the first order won't effect selecting the second order (independent events).
b) Assuming that the choices are made without substitution, the likelihood of receiving both orders from restaurant D is equal
Accordingly, the Total Probability of receiving both orders from restaurant D, without substitution, is calculated as follows: 0.1436*0.1428 = 0.0205.
In other words, since the events are not independent from one another as they are in the first question, picking the first order has an impact on the second order.
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