Explanation:
tossing 2 coins at the same time, or one coin twice is the same scenario.
anyway, a probability is always the ratio
desired cases / all possible cases
when having 2 coin tosses, there are 2×2 = 4 total possible results (each toss has 2 possibilities, so 2 tosses have them 2×2 = 4 possibilities) :
head head
head tails
tail head
tail tails
how many of these 4 possible cases show at least one head ?
3 : head-head, head-tails, tails-head
so the probability to get at least one head is
3/4 = 0.75
formally calculated we would get this by saying either
this is NOT 2 times tail.
the probability of 2 times tails is
1/2 × 1/2 = 1/4 = 0.25
the probability for NOT 2 times tails is then
1 - 0.25 = 0.75
or by saying
this is either heads on the first coin and tails on the other, or tails on the first coin and heads on the other, or heads on both.
the probability of heads on the first and tails on the other coin is
1/2 × 1/2 = 1/4
the probability of tails on the first and heads on the other coin is
1/2 × 1/2 = 1/4
the probability of heads on both coins is
1/2 × 1/2 = 1/4
so, the total probability of all 3 cases is
1/4 + 1/4 + 1/4 = 3/4 = 0.75
you see : for an exclusive "or" condition we add the probabilities. for an exclusive "and" condition we multiply the probabilities.