"The probability of getting heads on a biased coin is 1/3. Sammy tosses the coin 3 times. Find the probability of getting two heads and one tail".
I thought that all you have to do is:
(1/3)(1/3)(2/3)
It makes sense to me, but it's not right...
Here are the possibilities:
HHT
HTH
THH
Each one has a probability of (1/3)(1/3)(2/3) = 2/27. For either-or probabilities, add the probabilities of the individual events.
I WOULD PUT IT AS A SIMPLE 1/3
use 3C2 (1/3)^2(2/3)1 in the calculator. (3c2 as in 3=number of trials, 2= number of successes, plug into the math>prob>ncr function. )
Well, sometimes math can be as tricky as a coin flip! Let's take a closer look at your calculation. You were right to multiply the probabilities together, so kudos for that! However, the order in which you get two heads and one tail can vary.
To find the correct probability, you need to consider all the possible ways you can get two heads and one tail. In this case, there are three ways: HHT, HTH, and THH. Each of these ways has the same probability of occurring, which is (1/3)(1/3)(2/3).
So to find the correct answer, you need to add up the probabilities of each of these possibilities:
(1/3)(1/3)(2/3) + (1/3)(2/3)(1/3) + (2/3)(1/3)(1/3)
Give it another try, and I'm sure you'll land on the right answer this time! Keep up the good work!
To find the probability of getting two heads and one tail when tossing a biased coin, you need to take into account the different combinations in which this can occur.
Let's break it down step by step:
1. Start by determining the probability of getting a head or a tail in a single coin toss. In this case, the probability of getting a head is 1/3, and the probability of getting a tail is 1 - (1/3) = 2/3.
2. To find the probability of getting two heads and one tail, you need to consider all the possible orders in which this can occur. For example, you could get heads on the first two tosses and a tail on the third toss, or you could get a tail first and then heads on the next two tosses.
To calculate this, you need to consider the different combinations of heads and tails that lead to two heads and one tail. There are three possible orders: HHT, HTH, and THH.
3. Calculate the probability for each order:
a. HHT: (1/3) * (1/3) * (2/3)
b. HTH: (1/3) * (2/3) * (1/3)
c. THH: (2/3) * (1/3) * (1/3)
4. Add up the probabilities for each order:
Probability = (1/3) * (1/3) * (2/3) + (1/3) * (2/3) * (1/3) + (2/3) * (1/3) * (1/3)
Simplifying the equation will give you the final probability of getting two heads and one tail when tossing the biased coin three times.