Question

The following contingency table shows the number of two-bedroom apartments grouped by monthly rent and location.

Monthly Rent                      York       Lancaster      Dover              Total
$600 to under $700              6              15                     9                      30
$700 to under $800              30                  21                   24                     75
$800 to under $900             15                  18                    12                      45
Total   51                   54                   45                     150

The probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster is ________.

		0.59
		0.72
		0.85
		0.63

Answer 1

Given,

Monthly rent	York	Lancaster	Dover	Total
$600 to Under $700	6	15	9	30
$700 to Under $800	30	21	24	75
$800 to Under $900	15	18	12	45
Total	51	54	45	150

A : Event of selecting apartment from this group has a monthly rental from $700 to under $800

Probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 = P(A)

P(A) = Number of apartments from this group has a monthly rental from $700 to under $800 / Total number of apartments from this group = 75/150

B : Event of selecting apartment from this group is located in Lancaster

Probability that a randomly selected apartment from this group is located in Lancaster = P(B)

P(B) = Number of apartments from this group is located in Lancaster / Total number of apartments from this group = 54/150

A and B : Event of selecting apartment from this group has a monthly rental from $700 to under $800 and is located in Lancaster

P(A and B) = Probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 and  is located in Lancaster = Number of apartments from this group has a monthly rental from $700 to under $800 and s located in Lancaster / Total number of apartments from this group = 21/150

Probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster = P(A or B)

By Addition theorem of probability :

P(A or B) = P(A) + P(B) - P(A and B) = 75/150 + 54/150 - 21/150 = (75+54-21)/150 = 108/150 = 0.72

The probability that a randomly selected apartment from this group has a monthly rental from $700 to under $800 or is located in Lancaster is 0.72

Ans : 0.72