A coin is tossed two times. find the probability of getting both heads and both tails.

Solution:

Given a coin is tossed twice

To find the probability that both are heads

ASSUMPTIONS WE NEED TO RECOGNISE:

The coin is FAIR, that is not biased in any manner such that if the coin is flipped a lot of times, an equal number of HEADS and TAILS will result

FACTS WE NEED TO UNDERSTAND:

When we toss a coin we get either a HEAD or a TAIL. The Probability of either is the same, which is 0.5 or 50%.

Each flip of the coin is an INDEPENDENT EVENT, that is the outcome of any coin flip, has no impact whatsoever on the outcome of any other coin flip. Putting that another way, we cannot predict the outcome of a coin flip based on the outcome of any previous flip.

ANALYSIS:

P(First coin flip = HEADS) = 0.5 = 50%

P(Second coin flip = HEADS) = 0.5 = 50% (not dependent on the previous coin flip)

∴P(Both Coin Flips = HEADS) = (0.5)*(0.5) or (1/2)*(1/2) = (1/4) = (0.25) = 25%

Another approach:

If we tabulate the possibilities of the outcomes of the two coin flips we get:

Note that each of the four combinations is equally likely as P(HEADS) = P(TAILS) = 0.5

There are 4 possible outcomes shown, being (H, H), (H, T), (T, H), and (T, T).

Only one option is of the four is (HEADS, HEADS), so P(FLIP 1 and FLIP 2 = HEADS, HEADS) = (1/4) = 0.25 = 25%

Summary:

When we flip a coin twice, the Probability of both coin flips returning HEADS is 0.25 or 25%

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A coin is tossed two times. Find the probability of getting both heads and both tails.

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