An unfair coin is weighted so that heads come up one third a

An unfair coin is weighted so that \"heads\" come up one third as often as \"tails\". What probability should be assigned to the outcome \"heads\" to reflect this weighting?

Solution

Here,

P(heads) = 1/3 P(tails)

Now, their probabilities must add up to 1,

P(heads) + P(tails) = 1

Hence,

1/3 P(tails) + P(tails) =1

(4/3) P(tails) = 1

Thus,

P(tails) = 3/4

Now,

P(heads) = 1/3 P(tails)

P(heads) = 1/3 (3/4)

P(heads) = 1/4 = 0.25 [ANSWER]