Question

a coin is altered so that the probability that it lands on heads is less than 1/2 and when the coin is flipped four times, the probability of an equal number of heads and tails is 1/6. what is the probability that the coin lands on heads?

Answer 1

The probability that the coin lands on heads (3-√3)/6.

What is meant by the probability?

• Probability is a branch of mathematics that deals with numerical descriptions of the how likely an incident is to occur or how likely a proposition is to be true.

For the given question;

Let x represent the likelihood of flipping heads. As a result, the probability of tossing tails is (1-x).

The probability of tossing two heads and two tails is equivalent to the number of aspects to flip it multiplied by the product of a probabilities of each coin flip.

6x²(1 - x)² = 1/6

On solving,

x²(1 - x)² = 1/36

Taking square root both sides.

x(1 - x) = ±1/6

Because both x and (1-x) seem to be non negative for the preferred probability x, we only need to take into account the positive root.

x(1 - x) = 1/6

Re arranging.

6x² - 6x + 1 = 0

Find the roots of the quadratic equation using the quadratic formula as;

(3±√3)/6

Using the quadratic formula, the roots of the this equation are (3±√3)/6.

Thus, as the probability of heads becomes less than half, the answer is (3-√3)/6.

To know more about the probability, here

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