In a village all the people speak Hausa or English or both. If \( 97 \% \) speak Hausa and \( 64 \% \) speak English, what percentage speak both languages?

To determine the percentage of villagers who speak both Hausa and English, we can use the principle of **inclusion-exclusion** for sets. Let's denote: - \( P(H) \) as the percentage of people who speak Hausa. - \( P(E) \) as the percentage of people who speak English. - \( P(H \cap E) \) as the percentage of people who speak both Hausa and English. Given: - \( P(H) = 97\% \) - \( P(E) = 64\% \) - All villagers speak either Hausa, English, or both, which means \( P(H \cup E) = 100\% \). The inclusion-exclusion principle states: \[ P(H \cup E) = P(H) + P(E) - P(H \cap E) \] Substituting the known values: \[ 100\% = 97\% + 64\% - P(H \cap E) \] Solving for \( P(H \cap E) \): \[ P(H \cap E) = 97\% + 64\% - 100\% = 161\% - 100\% = 61\% \] **Therefore, 61% of the villagers speak both Hausa and English.** **Answer:** 61 % of the people in the village speak both Hausa and English.