Question

A thick coin has probability $\frac{3}{7}$of falling heads, $\frac{3}{7}$of falling tails, and $\frac{1}{7}$of standing one edge. Show that if it is tossed repeatedly it has probability 1 of

Eventually standing on edge.

Short answer

Answer

The probability that the coin stands on the edge is 1.

Step-by-step solution

Given Information

A thick coin has probability $\frac{3}{7}$of falling heads, $\frac{3}{7}$of falling tails, and$\frac{1}{7}$ of standing on edge.

Definition of Independent Event

The events are said to be independent when the occurrence or non-occurrence of any event does not have any effect on the occurrence or non-occurrence of the other event.

Finding the probability that the coin lands on edge

The probability that the coin doesn’t land on edge is $\frac{6}{7}$and when the toss is done -times, the probability of not falling on edge is ${\left(\frac{6}{7}\right)}^n$.

This implies that the probability of landing on edge at least one time is$1-{\left(\frac{6}{7}\right)}^n$.

As the number of tosses increase the value of ${\left(\frac{6}{7}\right)}^n$gets closer to 0 and the probability eventually becomes 1.