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The Palestinians were under British rule (de facto and official) for only 31 years, from 1917-1948. During this time period, the British changed the primary language of official school instruction from Ottoman Turkish to Arabic. English was the sole foreign language on offer, but instruction was limited. A typical student might study English for four years.
Despite the end of British Rule, English remains a critical part of the Palestinian educational system.
As a result, there are certainly plenty of Palestinians who are fluent in English, but their primary language has always been Arabic.