Question

a survey was given to students asking whether they watch movies at home using netflix, amazon prime, or hbo max. the results are below:
376 students only use hbo max.
394 students only use amazon prime.
361 students only use netflix.
320 students said they were using only netflix and hbo max.
203 students said they were using only netflix and amazon prime.
261 students said they were using only amazon prime and hbo max.
343 students said they were using all three.
289 students said none of these.
fill in the following venn diagram with the cardinality of each region then answer the questions below.
how many students use exactly two of them?
how many students use netflix or hbo max, but not amazon prime?
how many students use amazon prime and hbo max?
how many students were surveyed?
how many students use netflix, amazon prime, or hbo max?

Explanation:

Step1: Identify regions for each part

• Let's match the given data to the Venn - diagram regions.
• Region I: Only Netflix = 361
• Region II: Only Netflix and Amazon Prime = 203
• Region III: Only Amazon Prime = 394
• Region IV: Only Netflix and HBO Max = 320
• Region V: All three = 343
• Region VI: Only Amazon Prime and HBO Max = 261
• Region VII: Only HBO Max = 376
• Region VIII: None of them = 289

Step2: Calculate number of students using exactly two

The students using exactly two services are in regions II, IV, and VI.
Sum = 203 + 320+261 = 784

Step3: Calculate number of students using Netflix or HBO Max, but not Amazon Prime

This includes regions I, IV, and VII.
Sum = 361+320 + 376=1057

Step4: Calculate number of students using Amazon Prime and HBO Max

This includes regions VI and V.
Sum = 261+343 = 604

Step5: Calculate total number of students surveyed

Sum of all regions = 361+203+394+320+343+261+376+289 = 2547

Step6: Calculate number of students using Netflix, Amazon Prime, or HBO Max

Sum of regions I - VII = 361+203+394+320+343+261+376=2258

Answer:

• How many students use exactly two of them? 784
• How many students use Netflix or HBO Max, but not Amazon Prime? 1057
• How many students use Amazon Prime and HBO Max? 604
• How many students were surveyed? 2547
• How many students use Netflix, Amazon Prime, or HBO Max? 2258