Chapter 7, Problem 18PT2

To determine

To find: The probability that randomly chosen calf was female or born in the night.

Answer to Problem 18PT2

The probability is $\frac{369}{513}$ .

Explanation of Solution

Given:

The table is:

	Day	Evening	Night	Total
Males	129	15	117	261
Females	118	18	116	252
Total	247	33	233	513

Calculation:

The probability that randomly chosen calf was female or born in the night could be calculated as:

  $\begin{array}{c}P\left(\begin{array}{l}\text{Female or born }\\ \text{at night}\end{array}\right)=P\left(\text{Female}\right)+P\left(\text{Born at night}\right)-P\left(\text{Female and born at night }\right)\\ =\frac{223}{513}+\frac{262}{513}-\frac{116}{513}\\ =\frac{369}{513}\end{array}$

Thus, the required probability is $\frac{369}{513}$ .