Although the odds were against Israel, they managed to defeat the Arabs and benefit from the wards because of their strengths and Arab weaknesses. Israel was successful because they were organized and disciplined and they had help from foreign powers.
Arabs didn't want to recognize the state of Israel. During the war of 1948-9, the Arab states were weak and divided. Their defeat was because of their poor leaders and they had no planned attack. They were disorganized and had no coordination. Arab armies weren't prepared well enough against Israeli forces. They weren't trained well or didn't have good equipment to fight. Arab states had underestimated Israeli forces and the fact that Israelis had more experience in war gave them an advantage. Jewish soldiers were well disciplined in comparison to the Arab soldiers and had more experience than the Arabs because of their experience in world war two. Unlike the Arabs, they had good leaders and had coordination and organization.
Israelis were motivated to fight to save their new country. Also, Israelis were always prepared for war and more and more Jews from different parts of the world migrated to Israel to help out.
Israelis had planned attacks in the war of 1956 to strengthen their position. Israelis were able to capture the Sinai Peninsula but had to give it back in 1957. Israelis had foreign support from Britain and France.
In the 1967 war, again, Israeli strengths and Arab weaknesses led to Arab defeat. Israelis effectively planned a surprised attack which took Arab states by surprise. By the first day, Israeli troops had destroyed Arab air forces and had full control over the skies. This shows again, that Israelis had the best-equipped troops in the Middle East and had aid from the US. They had US electronic equipment...