Question

A coin is weighted so that there is a 58% chance that it will come up "heads" when flipped. The coin is flipped four times. Find the probability of getting two "heads" and two "tails". Round your answer to four decimal places.

Answer 1

P(A) =Probability of heads

P(B) = Probability of tails

P(B)= 1 - P(A) = 1 - 58 = 42%

The events are independent, so, let's assume that we flip the coin and the first two results are heads, so:

P(A) =0.58

Now, let's assume the last two results are tails so:

P(B) = 0.42

Therefore:

$\begin{gathered} P(A\cap A\cup B\cap B)=P(A)\cdot P(A)\cdot P(A)+P(B)\cdot P(B) \\ P(A\cap A\cup B\cap B)=0.58\cdot0.58+0.42\cdot0.42=0.3364+0.1764=0.5128 \end{gathered}$