Biased

Level 1

I have a biased coin. It comes up heads more often than tails.

When I throw it twice, the chances that it will give 2 heads is the same as the chances that it will give at least 1 tails.

The probability that this biased coin will get heads on a single throw is:

Note: Choose the closest and most accurate option.

50% 80% 70% 90% 100% 60%

1 solution

Jordan Cahn
Nov 28, 2018

Let $p$ be the probability of the coin landing heads. Note that there are only two possibilities with two flips: either they are both heads or there is at least one tails. The probability of the former is $p^2$ and, therefore, the probability of the latter is $1-p^2$ . It is given that these two probabilities are equal: $\begin{aligned} p^2 &= 1-p^2 \\ 2p^2 &= 1 \\ p^2 &=\frac{1}{2} \\ p &= \frac{\sqrt{2}}{2} \approx 0.707 \approx \boxed{70\%} \end{aligned}$

Biased

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