Question

at a movie theater, there are a total of 350 customers. each customer is located in either theater a, theater b, or theater c. if one of these customers is selected at random, the probability of selecting a customer who is located in theater a is 0.48 and the probability of selecting a customer who is located in theater b is 0.24. how many customers are located in theater c?
a. 28
b. 40
c. 84
d. 98

Explanation:

Step1: Find probability of theater C

The total probability is 1. So probability of C, \( P(C) = 1 - P(A) - P(B) \).
Given \( P(A) = 0.48 \), \( P(B) = 0.24 \), so \( P(C)=1 - 0.48 - 0.24 = 0.28 \).

Step2: Calculate number of customers in C

Total customers = 350. Number of customers in C = \( 350\times P(C) \).
Substitute \( P(C) = 0.28 \), so \( 350\times0.28 = 98 \)? Wait, no, wait. Wait, wait, let's recheck. Wait, 350 0.28: 3500.2=70, 3500.08=28, so 70+28=98? But wait, the options have A.28, B.40, C.84, D.98? Wait, no, wait, maybe I misread. Wait, the problem says "how many customers are located in theater C?". Wait, total customers 350. Probability of A is 0.48, so number in A is 3500.48=168. Probability of B is 0.24, so number in B is 3500.24=84. Then number in C is 350 - 168 - 84 = 350 - 252 = 98? Wait, but 3500.28 is 98. But wait, the options: A.28, B.40, C.84, D.98. Wait, but maybe I made a mistake. Wait, no, let's recalculate. 350 0.48: 35048/100 = (35048)/100 = (16800)/100 = 168. 3500.24 = 84. Then 350 - 168 - 84 = 350 - 252 = 98. So the answer is D? Wait, but the option D is 98. Wait, but let me check again. Wait, the probability of C is 0.28, so 3500.28 = 98. Yes. So the number of customers in theater C is 98. Wait, but the options: A.28, B.40, C.84, D.98. So D is 98. Wait, but maybe I misread the problem. Wait, the problem says "how many customers are located in theater C?". So yes, 350(1 - 0.48 - 0.24) = 350*0.28 = 98. So the answer is D.

Answer:

D. 98