Question

You flip a coin 3 times. let "x" represent the number of heads you obtain. find each of the following probabilities and leave your answers as a decimal rounded to three decimal places. p(x=0)=, p(x>1)=, p(x<1)=, p(x does not equal 3) =

Answer 1

To find the probabilities of getting certain numbers of heads when flipping a coin 3 times, we can use the binomial probability formula. The formula is P(x=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success. We can apply this formula to find p(x=0), p(x>1), p(x<1), and p(x does not equal 3).

Step-by-step explanation:

To find the probabilities in this scenario, we can use the binomial probability formula. The formula is P(x=k) = C(n,k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful outcomes, and p is the probability of success.

a) For p(x=0), we have P(x=0) = C(3,0) * (0.5)^0 * (0.5)^(3-0) = 1 * 1 * 0.125 = 0.125.

b) For p(x>1), we can calculate P(x>1) = P(x=2) + P(x=3) = C(3,2) * (0.5)^2 * (0.5)^(3-2) + C(3,3) * (0.5)^3 * (0.5)^(3-3) = 3 * 0.25 * 0.5 + 1 * 0.125 * 1 = 0.375.

c) For p(x<1), we can calculate P(x<1) = P(x=0) = 0.125.

d) For p(x does not equal 3), we need to find 1 - P(x=3) = 1 - C(3,3) * (0.5)^3 * (0.5)^(3-3) = 1 - 1 * 0.125 * 1 = 0.875.