Two coins are tossed simultaneously, find the probability of getting.1.atleast one head.2.at most one tail

If two coins are tossed simultaneously, you will have one of the possible results

with probability 1/4 each.

So, you'll have at least one head if you have HH, HT or TH, i.e. with probability 3/4.

Similarly, you have at most one tail if you get HH, HT or TH, so the probability will be the same.

In fact, both claims (at least one head and at most one tail) are verified by the same set of outputs HH, TH, HT, since they're not satisfied only by the output HH.

So, if those claims are not satisfied with probability 1/4, they're satisfied with probability 3/4.

step-by-step explanation:

this can be solved first with pythagorean theorem, which tells us to square both legs of the triangle and sum it. this will be equal to the square of the hypotenuse.

the hypotenuse is the side "opposite" the 90 degree angle, which is x.

so we can write using pythagorean theorem,

simplifying:

to further simplify this radical, we need to use the property  

thus