Alex V. answered • 07/19/22
PhD student with 5+ years of teaching experience
For the first question, the probability of getting three heads in three tosses, you simply multiply 1/2 x 1/2 x 1/2 to get 1/8.
The second asks the probability of getting two heads and one tail in any order. Your answer is correct, it's 3/8. To get this number you look at the number of possible combinations of outcomes, i.e. HHH, TTT, HHT, TTH, etc. There are 8 possible combinations, and three of them have two heads, giving us a probability of 3/8.
The third question asks for the probability of getting at least one tails. The way to answer this is similar to the last question. We know there are 8 possible combinations of how the coin can land in three flips. How many of those don't include a single tails outcome? Only one, where we get heads three times. So that's 1 possible outcome among 8 possibilities, or a probability of 1/8.
The last question asks for the probability of at least two heads. Again, this question follows the same pattern. We know there are 8 possible combinations. How many include at least two heads? From the second question we know there are 3 ways to get exactly two heads. But this says at least so it includes the possibility of getting all 3 heads. But there's only one way to do that, HHH. And 3+1=4 possible ways that have at least two heads giving us a probability of 4/8 or 1/2 that we get at least two heads on three flips.
Hope that helps!
