A coin is tossed four times. Find the probability of each of the following:
P(exactly 1 head)
I know we have to use to this formula
p(x=0)=nCk(p)^k(1-p)^n-k
How do you find P? if n=4
To find the probability, we need to know the values of n, k, p, and (1-p) in the formula you mentioned.
In this case, n = 4 because the coin is tossed four times.
To find the probability of exactly 1 head, k = 1.
p represents the probability of getting a head in a single toss of the coin. Since it is a fair coin, there is an equal chance of getting heads or tails, so p = 0.5 (or 1/2).
(1-p) represents the probability of getting a tail in a single toss of the coin. Again, since it is a fair coin, it is also 0.5 (or 1/2).
Now we can substitute these values into the formula:
P(exactly 1 head) = 4C1 * (0.5)^1 * (0.5)^(4-1)
In this expression:
4C1 represents "4 choose 1," which can be calculated as 4! / (1! * (4-1)!). This simplifies to 4.
(0.5)^1 represents the probability of getting 1 head.
(0.5)^(4-1) represents the probability of getting 3 tails.
Let's calculate the probability:
P(exactly 1 head) = 4 * 0.5 * 0.5^3
P(exactly 1 head) = 4 * 0.5 * 0.125
P(exactly 1 head) = 0.25
So the probability of getting exactly 1 head when tossing the coin four times is 0.25 or 25%.