sets and probability

[luvbug]

Problem: A survey of 100 students majoring in languages was completed. It was found that 50 students read French, 60 students read Spanish, and 70 students read French OR Spanish. How many students read Spanish but not French.

My work: I used a Venn diagram with 70 in the middle and 20 on the French side and 10 on the Spanish side. However, this doesn't work because that shows that 70 read French AND Spanish. My problem specifies OR. Not for sure what formula or Venn diagram to use. Thanks.

 

[Deleted member 4993]

Problem: A survey of 100 students majoring in languages was completed. It was found that 50 students read French, 60 students read Spanish, and 70 students read French OR Spanish. How many students read Spanish but not French.

My work: I used a Venn diagram with 70 in the middle and 20 on the French side and 10 on the Spanish side. However, this doesn't work because that shows that 70 read French AND Spanish. My problem specifies OR. Not for sure what formula or Venn diagram to use. Thanks.

There are 30 students (100-70) who do not study French or Spanish.

The part in the middle of your Venn diagram (where you have 70) indicates the number of students who studies both (French and Spanish). That number should be 40 (How?).

 

[luvbug]

Okay. Let me see if I get this now. 60 + 50 = 110, subtract 70 from that = 40 (those 70 were part of the 110). So, the 40 goes in the middle of the Venn diagram. Then 30 goes outside, 10 goes for Spanish and 20 for French. Think I got it! Thanks,

 

[Deleted member 4993]

Okay. Let me see if I get this now. 60 + 50 = 110, subtract 70 from that = 40 (those 70 were part of the 110). So, the 40 goes in the middle of the Venn diagram. Then 30 goes outside, 10 goes for Spanish and 20 for French. Think I got it! Thanks,

It should be other way - 10 goes for French_only and 20 goes for Spanish_only.