Toss a Coin

Probability Level 2

When flipping an unfair coin once, what is the probability of the coin coming up heads plus the probability of the coin coming up tails?

\frac{1}{4}

\frac{1}{2}

\frac{3}{4}

2 solutions

Mostakim Shakil
Mar 14, 2016

*Since the possible outcomes are heads or tails, so we can expect that the probability to be 100% or 1. *

This is not really a solution. It just restates the problem and the answer.

Colin Carmody - 5 years, 3 months ago

Yeah not really looks like a solution but think .. If you tossed up a coin, you must have a result which may be either heads or tails. So we are pretty sure about getting a result. Now here is the solution for you- As we flip the coin once, probability of getting heads is = $\frac{1}{2}$ , probability of getting tails is = $\frac{1}{2}$ . To calculate either-or probabilities, we have to add individual probabilities. So, probability of getting either heads or tails is = $\frac{1}{2}$ + $\frac{1}{2}$ = 1

Mostakim Shakil - 5 years, 3 months ago

Hi Colin & Mostakim......I've written a more technical solution above. Enjoy!

tom engelsman - 8 months, 4 weeks ago

Tom Engelsman
Sep 20, 2020

Let $p$ be the probability of the unfair coin turning up heads and $1-p$ be the probability of turning up tails ( $p \neq \frac{1}{2}$ ). Also, let $H$ and $T$ be the events of turning up heads and tails respectively (which are mutually exclusive $\Rightarrow H \cap T = \emptyset$ ). We are interested in the probability:

$P(H \cup T) = P(H) + P(T) - P(H \cap T) = p + (1-p) + 0 = \boxed{1}.$

Toss a Coin

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