Question-45

A random experiment consists of throwing \(100\) fair dice, each having six faces numbered \(1\) to \(6\). An event \(A\) represents the set of all outcomes where at least one of the dice shows a \(1\). Then, \(P( A) =\)

• \(0\)

• \(1\)

• \(1-\left(\cfrac{5}{6}\right)^{100}\)

• \(\left(\cfrac{5}{6}\right)^{100}\)

NoteAnswer

• \(0\)

• \(1\)

• \(1-\left(\cfrac{5}{6}\right)^{100}\)

• \(\left(\cfrac{5}{6}\right)^{100}\)

NoteSolution

The event \(A^{c}\) is the one where none of the dice shows a \(1\). For a single dice to not show a \(1\), the probability is \(\cfrac{5}{6}\). Assuming independence, the probability of none of the dice showing a \(1\) is \(P\left( A^{c}\right) =\left(\cfrac{5}{6}\right)^{100}\). It follows that \(P( A) =1-\left(\cfrac{5}{6}\right)^{100}\).