Drums And Cymbals

Head Double

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Probability of double head on biased coin toss?

Two indentical biased coins are each more likely to land showing heads than tails. The two coins are tossed together and the outcome recorded. After a large number of trials it is observed that the probability that they land showing a head and a tail is 0.48.

What is the probability of getting two heads in a single throw of these two coins?

If the coins were not biased then the probability of one throw landing either a head or a tail would be equal, at 0.5 each.

With the biased coins, let the probability of landing a head on a single throw of one coin be Ph = 0.5+b which makes the probability of landing a tail on one such throw = Pt = 0.5-b (Ph + Pt must = 1)

There are two ways to throw a head and a tail; either “a head and a tail” or “a tail and a head”. The probability of achieving a head and a tail on one throw of two coins is therefore (Ph x Pt) + (Pt x Ph)

= (0.5 + b).(0.5 – b) + (0.5 – b).(0.5 + b).

= 2(0.25 - b²) = (0.5 – 2b²) = 0.48 so 2b² = 0.02 or b² = 0.01 giving b = 0.1

The probability of throwing a head on a single throw is 0.5+b so the probability of throwing two heads on a single throw of the two coins is (0.5 + b)² = 0.6² = 0.36

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« Previous12Next »

Probability of double head on biased coin toss?

Two indentical biased coins are each more likely to land showing heads than tails. The two coins are tossed together and the outcome recorded. After a large number of trials it is observed that the probability that they land showing a head and a tail is 0.48.

What is the probability of getting two heads in a single throw of these two coins?

If the coins were not biased then the probability of one throw landing either a head or a tail would be equal, at 0.5 each.

With the biased coins, let the probability of landing a head on a single throw of one coin be Ph = 0.5+b which makes the probability of landing a tail on one such throw = Pt = 0.5-b (Ph + Pt must = 1)

There are two ways to throw a head and a tail; either “a head and a tail” or “a tail and a head”. The probability of achieving a head and a tail on one throw of two coins is therefore (Ph x Pt) + (Pt x Ph)

= (0.5 + b).(0.5 – b) + (0.5 – b).(0.5 + b).

= 2(0.25 - b²) = (0.5 – 2b²) = 0.48 so 2b² = 0.02 or b² = 0.01 giving b = 0.1

The probability of throwing a head on a single throw is 0.5+b so the probability of throwing two heads on a single throw of the two coins is (0.5 + b)² = 0.6² = 0.36

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