For safety reasons, four different alarm systems were installed in the vault containing the safety deposit boxes at a Beverly Hills bank. Each of the four systems detects theft with a probability of .99 independently of the others.

1.) What is the probability that when a theft occurs, all four systems will detect it?

(a) (.99)4
(b) (.99) * 4
(c) (.01)4
(d) (.01) * 4
(e) None of the above.

I figured it would (b) (.99)*4, however a and b seem like the same answer?

2.)The bank, obviously, is interested in the probability that when a theft occurs, at least one of the four systems will detect it. This probability is equal to:

(a) (.99)4
(b) (.01)4
(c) 1- (.99)4
(d) 1- (.01)4
(e) 1- (.01)*4

Clueless on this one.

3.) A coin is tossed three times, or until the first "heads" appears, whichever occurs first. Which of the following is the sample space for this random experiment?

(a) S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}
(b) S = {H, TH, TTH}
(c) S = {H, TH, TTH, TTT}
(d) S = {H, HH, HHH}
(e) S = {H, HT, HHT, HHH}

I'm going with e, due to a simulation example I did, is that correct?

4.) Only 40% of the students in a certain liberal arts college are males. If two students from this college are selected at random, what is the probability that they are of the same gender?

(a) .96
(b) .52
(c) .48
(d) .36
(e) .16

I'm going between b or c, because there is high chance, but not super high that they will be both females..is B correct?