Ballet arm positions for 3rd and 4th are slightly different depending on the school or method being taught. I like to teach the picture below and include the fourth position in the video. I say that there are two options for fourth: open like in the picture and closed like the video. Third position in the picture is important for pirouette turning.
Ballet vocabulary and action cards. Study these cards to better understand what the body is suppose to be doing during the movement. I love these cards created by @grace.on.pointe and aballeteducation.com.