第一步：获取随机值

sum = 20+61+97+39+32+48+10+20+48+78 = 453

share1 = 20/453 = 0.04415011
...
share10 = 0.17218543

第二步：计算红包金额

a1 = share1 * 100 = 0.04415011 * 100 = 4.415011
...
a10 = share10 * 100 = 0.17218543 * 100 = 17.218543

代码

$('#submit').click(function(){
  function getRandomInt(min, max) {
    return Math.floor(Math.random() * (max - min)) + min;
  }

  function getNextItemKey(currentKey, count) {
    if (currentKey > count) {
      throw 'Error: currentKey > count';
    }
    if (currentKey != count) {
      return currentKey + 1;
    } else {
      return 1;
    }
  }

  var count = $('#count').val();
  var amount = $('#amount').val();
  if (!count) {
    alert('红包个数必须填写');
    return false;
  }
  if (!amount) {
    alert('总金额必须填写');
    return false;
  }
  if (amount / count < 0.01) {
    alert('单个红包金额不可低于0.01元，请重新填写金额');
    return false;
  }
  amount = amount * 100;
  var items = [];
  for (var i = 0; i < count; ++ i) {
    items[i] = getRandomInt(1, 100);
  }
  var itemAmounts = [];
  var sum = items.reduce(function(pv, cv) { return pv + cv; }, 0);
  var currentAmount = 0;
  for (var i = 0; i < count; ++ i) {
    if (i !== count - 1) {
      itemAmounts[i] = Math.floor(items[i] / sum * amount);
      currentAmount += itemAmounts[i];
    } else {
      itemAmounts[i] = amount - currentAmount
    }
  }

  for (var i = 0; i < count; ++ i ) {
    if (itemAmounts[i] > 0) {
      continue;
    }
    var nextKey = getNextItemKey(i, count);
    var diff = 1 - itemAmounts[i];
    itemAmounts[i] = 1;
    itemAmounts[nextKey] -= diff;
  }

  for (var i = 0; i < count; ++ i ) {
    itemAmounts[i] = itemAmounts[i] / 100;
  }

  alert(itemAmounts.join('元'));

});