When you say "I want to make sure that I solved them correctly, the tasteful, less suspicious thing to do is to list YOUR solutions, so that the responder can either say "that one's correct" or else show you how to do it.
1). HHH HHT HTH HTT THH THT TTH TTT a). The probability of each one is 1/8 = 12.5% . b). There's only one of those on the list. 12.5% c). 12.5% d). There are 3 ways that can happen. 3/8 = 0.375 = 37.5%
2). There are 16 possible outcomes. a). Prob of each outcome is 1/16 = 0.0625 = 6.25% . b). There's only 1 way that can happen, so it's 6.25% . c). There's only 1 way that can happen, so it's 6.25% . d). There are 6 ways that can happen. Prob = 6/16 = 37.5% e). There are 4 ways that can happen. Prob = 4/16 = 25%
Since we know that the 38 is being bisected (which we can tell by the fact that the line hits it perpendicularly), we know that from the intersection to the edge of the circle is 19. From this we can create a right triangle in which the legs are 10 and 19 and the hypotenuse is a radius of the circle. Since x is also a radius of the circle, all we have to do is use that information to find the hypotenuse using the Pythagorean Theorem and we have x.
Pythagorean Theorem + = + = 100 + 361 = 461 = x = or about 21.47