Question

For Chapter 2 through Chapter 14, the Cumulative Review Exercises include topics from preceding chapters. For this chapter, we present a few calculator warm-up exercises, with expressions similar to those found throughout this book. Use your calculator to find the indicated values.

Six Children Jule Cole is a founder of Mabel’s Labels, and she is the mother of six children. The probability that six randomly selected children are all girls is found by evaluating\({0.56^6}\). Find that value.

Short answer

The probability (or likelihood) that all the six randomly selected children are females given by \({0.5^6}\) is equal to 0.015625.

Step-by-step solution

Given information

The founder of Mabel’s Labels, Jule Cole, has six children. The probability of all six randomly chosen children being female is given by \({0.5^6}\).

Powers and exponents

Thepowerof a number is computed by multiplying the number byitself, repeated a number of times.

The total number of times a numerical value is multiplied by itself is called theexponent, and the numerical value is called thebase number.

It is denoted as \({\left( {{\rm{base}}\;{\rm{number}}} \right)^{{\rm{exponent}}}}\).

  Determining the value

The probability that all six randomly selected children are girls is given by\({0.5^6}\).

Here, thebase numberis0.5, and theexponent is6.

\(\begin{array}{c}{0.5^6} = 0.5 \times 0.5 \times 0.5 \times 0.5 \times 0.5 \times 0.5\\ = 0.015625\end{array}\)

Hence, the value is obtained to be equal to 0.015625.