A coin is loaded in such way that a tail is three times as likely to occur as a head. If the coin is flipped twice. Find the probability that two heads occur
From your data, with four tosses, you would get 3 tails and one head by chance.
The probability of one head would then be 1/4.
If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.
To find the probability of getting two heads when flipping a loaded coin, we first need to determine the probability of getting a head and a tail.
Given that a tail is three times as likely to occur as a head, we can assume that the probability of getting a head (H) is \( \frac{1}{4} \) (since 1 unit of probability corresponds to 1 part out of 4 in total), and the probability of getting a tail (T) is \( \frac{3}{4} \) (since 3 units of probability correspond to 3 parts out of 4 in total).
When flipping a coin twice, we have four possible outcomes: HH, HT, TH, and TT. Since we want to find the probability of getting two heads, we only need to consider the case of HH.
The probability of getting two heads (HH) is calculated by multiplying the probability of getting a head on the first flip (\( \frac{1}{4} \)) with the probability of getting a head on the second flip (\( \frac{1}{4} \)):
\( P(HH) = P(H) \times P(H) = \frac{1}{4} \times \frac{1}{4} = \frac{1}{16} \).
Therefore, the probability that two heads occur when flipping the loaded coin twice is \( \frac{1}{16} \), or 0.0625, or 6.25%.