Question

suponha que um ponto atingisse aleatoriamente algum ponto da circunferência abaixo. qual é a probabilidade de atingir a região sombreada? draw

Explanation:

Step1: Calculate the measure of the shaded arc

The total degrees in a circle is \(360^{\circ}\). The un - shaded part adjacent to the \(64^{\circ}\) angle is a straight line (semicircle, \(180^{\circ}\)). But we can also use the formula for probability of a sector. The probability \(P\) of a point landing in a sector of a circle is given by \(P=\frac{\theta}{360}\), where \(\theta\) is the central angle of the sector. Here, \(\theta = 180 - 64=116^{\circ}\)

Step2: Calculate the probability

Using the formula \(P=\frac{\theta}{360}\), substitute \(\theta = 116^{\circ}\). So \(P=\frac{116}{360}\)
Simplify the fraction: \(\frac{116\div4}{360\div4}=\frac{29}{90}\)

Answer:

\(\frac{29}{90}\)