On Saturday morning, Malachi will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.2, what is the probability that Malachi will return home at the end of the day on the following Monday?

0.008

0.128

0.488

0.512

0.640

If n is a position integer and r is the remainder when (n-1)(n+1)is divided by 24, what is the value of r ?

1)      2 is not a factor of n

2)      3 is not a factor of n

1.0.8*0.8*0.2=0.128

2.You can use a specific integer to get the result, we use 5 for example. And obviously the remainder r equals 0

第二题

连续三个整数中必有一个是3的倍数，由条件2）n不是3的倍数 => （n-1）和（n+1）中一定有一个是3的倍数
条件1）n不是偶数 => （n-1）和（n+1）必均为偶数，且中间有一个是4的倍数 => 2的倍数×4的倍数 =>(n-1)(n+1)必为8的倍数

所以，必为24的倍数