The first correct probability is 1/5,
The probability of being incorrect is 4/5.
The second correct probability is 1/4, and the total probability is 4/5× 1/4 = 1/5.
The probability of being incorrect is 3/4.
The third correct probability is 1/3, and the total probability is 4/5× 3/4× 1/3 = 1/5.
The probability of being incorrect is 2/3.
The fourth correct probability is 1/2, and the total probability is 4/5× 3/4× 2/3×1/2 =1/5.
The incorrect probability is 1/2.
The fifth correct probability is 1, and the total probability is 4/5× 3/4× 2/3×1/2×1=1/5.
(2) The probability of opening the door three times =1/5+1/5+1/5 = 3/5.