Question

in a survey of a community it was found that 85 percent people like summer season if there were not any people who did not like both seasons i )represent in venn diagram ii) what percent were there who like both the seasons iii) what percent were there who like only one season​

Answer 1

Answer:

I think you mean ‘one or the other’ rather than ‘both’ in the sentence,’If there who…’

Accepting that, let W be those who like W and S be those who like summer.

P(W or S) = 1

Also P(W or S) = P(W) + P(S) - P(W and S).

Hence, 1 = 0.85 + 0.65 - P(W and S).

Hence, P(W and S) = 1.5 - 1 = 0.5.

The percent who like both is P(W and S)= 50%

(ii)The percent who like winter only is 85% - 50% = 35%.

Another method :-

So, since we know that zero people liked neither, there must be 100%-85%=15% of the people who do not like winter and so like only summer. The remaining 65% who like summer must also like winter.