Rooms NO of units
1 471
2 1470
3 11715
4 23468
5 24476
6 21327
7 13782
8+ 15647
compute the following conditional probablilites directly that is, do not use the conditional probability rule. For a U.S. housing unit selected at random, determine
a. the probability that the unit has exactly four room.
b. the conditional probablility that the unit has exactly four rooms given that it has at least 2 room
c. the conditinal probability that the unit has at most four rooms, given that it has at least two rooms.
d. interpret your answers in parts (a)-(b) in terms of percentages.
Take a shot. What do you think. Hint: an Excel spreadsheet is very helpful for these types of problems.
To compute the conditional probabilities directly, we'll use the given information about the number of units in each room category.
a. Probability that the unit has exactly four rooms:
From the given information, we see that there are 23,468 units with four rooms. To calculate the probability, we divide the number of units with four rooms by the total number of units:
Probability = Number of units with four rooms / Total number of units
Probability = 23,468 / (471 + 1470 + 11715 + 23468 + 24476 + 21327 + 13782 + 15647)
b. Conditional probability that the unit has exactly four rooms given that it has at least two rooms:
To calculate this conditional probability, we need to consider the units with at least two rooms. From the given information, we know that there are:
(1470 + 11715 + 23468 + 24476 + 21327 + 13782 + 15647) units with two or more rooms.
Out of these, we need to find the number of units with exactly four rooms and divide it by the total number of units with at least two rooms.
Conditional Probability = Number of units with exactly four rooms and at least two rooms / Number of units with at least two rooms
c. Conditional probability that the unit has at most four rooms given that it has at least two rooms:
To calculate this conditional probability, we consider the units with at least two rooms, same as in part (b). We need to find the number of units with at most four rooms (which includes units with two, three, and four rooms) and divide it by the total number of units with at least two rooms.
Conditional Probability = Number of units with at most four rooms and at least two rooms / Number of units with at least two rooms
d. To interpret the answers in terms of percentages, you would multiply each probability value by 100 to convert them into percentages.