Question

A weighted coin has a 0.413 probability of landing on heads. What is the probability that it takes 3 flips for the first head to occur?

Answer 1

Explanation:

when we combine several independent events into one total event (AND combination), we multiply the individual probabilities to get the overall probabilty.

if the first head occurs at the 3rd flip we have the individual events

tail on the first flip

AND

tail on the second flip

AND

head on the third flip

P(heads) = 0.413

therefore,

P(tails) = 1 - P(heads) = 0.587

so, the total probability that it takes 3 flips for the first head to occur is

0.583 × 0.583 × 0.413 = 0.140374157... ≈ 0.14