题目

Marie, an 85-year-old woman who had been bedridden (卧床不起的) for 10 years, was granted her biggest wish to look at the sea again with help from East Coast Radio and Netcare 911.About 10 years ago, Marie had an unsuccessful back operation which left her bedridden. She then had to stay in an old age home and needed constant care. “The only time she could go outside was when she was taken to hospital over the years,” said Lucy, Marie’s daughter.Lucy wrote an e-mail to East Coast Radio in April asking them to help her take her mother to the beach because it was her biggest wish. She 盒子中装着有标数字1，2，3，4，5的上卡片各2张，从盒子中任取3张卡片，按3张卡片上最大数字的8倍计分，每张卡片被取出的可能性都相等，用ξ表示取出的3张卡片上的最大数字，求：（1）取出的3张卡片上的数字互不相同的概率；（2）随机变量ξ的概率分布和数学期望；（3）计分不小于20分的概率．