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
To find the probability of getting two heads when flipping a loaded coin twice, we can break down the problem into smaller steps.
Step 1: Determine the probability of getting a head (H) and a tail (T) on a single flip.
Given that a tail is three times as likely to occur as a head, we can assign probabilities to each outcome as follows:
- P(H) = x (probability of getting a head)
- P(T) = 3x (probability of getting a tail)
To find the value of x, we need to consider that the total probability for all outcomes must equal 1:
P(H) + P(T) = 1
Substituting the assigned probabilities:
x + 3x = 1
4x = 1
x = 1/4
Therefore, the probability of getting a head (H) on a single flip is 1/4, and the probability of getting a tail (T) is 3/4.
Step 2: Calculate the probability of two heads (HH) occurring in two flips.
Since the flips are independent events, we can multiply the probabilities of individual events to find the probability of two heads occurring consecutively:
P(HH) = P(H on flip 1) × P(H on flip 2)
= (1/4) × (1/4)
= 1/16
Therefore, the probability of getting two heads (HH) when flipping a loaded coin twice is 1/16 or 0.0625 (6.25%).