Question

What is the probability of flipping 3 coins on the same side, that is getting either all heads or all tails? Write the exact decimal answer without rounding.

Answer 1

Each coin has 2 outcomes when flipping (it may be head or tail), so the possibility to flip head is equal to possibility to flip tail and is $\frac{1}{2}$.

If you are flipping three times, then using the product rule you can conclude that the possibility to get three heads is equal to possibility to get three tails and is:
$\frac{1}{2} \cdot\frac{1}{2} \cdot\frac{1}{2} = \frac{1}{8} =0.125$

Answer 2

The probability of flipping 3 coins on the same side is $\boxed{\frac{1}{4}{\text{ or 0}}{\text{.25}}}.$

Further Explanation:

Explanation:

The probability of getting a head on tossing a coin is $P\left( H \right) = \dfrac{1}{2}.$

The probability of getting a tail on tossing a coin is $P\left( T \right) = \dfrac{1}{2}.$

The probability of getting 3 heads can be obtained as follows,

$\begin{aligned}P\left( H \right)&= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\\&= \frac{1}{8}\\\end{aligned}$

The probability of getting 3 tails can be obtained as follows,

$\begin{aligned}P\left( T \right) &= \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}\\&= \frac{1}{8}\\\end{aligned}$

The probability of flipping 3 coins on the same side can be obtained as follows,

$\begin{aligned}P\left({{\text{Head or Tail}}} \right)&= P\left( H \right) + P\left( T \right)\\&= \frac{1}{8} + \frac{1}{8}\\&= \frac{2}{8}\\&= \frac{1}{4}\\\end{aligned}$

The probability of flipping 3 coins on the same side is $\boxed{\frac{1}{4}{\text{ or 0}}{\text{.25}}}.$

Learn more:

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Answer details:

Grade: College

Subject: Mathematics

Chapter: Probability

Keywords: Probability, flipping, coins, 3 coins, flipping coins, same side, heads, tails, decimal, answer, rounding, all tails, all heads.