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Records from a random sample of dairy farms yielded the information below on the number of male and female calves born at various times of the day.

What is the probability that a randomly selected calf was
born in the night or was a female?
(a)369513

(b)485513

(c) 116513

(d)116252

(e) 116233

Short Answer

Expert verified

The correct answer is option (a)369513.

Step by step solution

01

Given information

The number of male and female calves born at various times of the day:


Day
Evening
Night
Total
Males
129
15
117
261
Females
118
18
116
252
Total
247
33
233
513
02

Explanation

The probability rules:
General addition rule:
P(AorB)=P(A)+P(B)-P(AandB)
Complement rule:
PAc=P(notA)=1-P(A)
Definition Conditional probability:
P(BA)=P(AB)P(A)=P(AandB)P(A)

03

Calculation

The probability is the number of favorable outcomes divided by the number of possible outcomes.
P(Born at night)=233513
P(Female)=262513
P(Female and born at night)=116513

Hence, the probability that a randomly selected calf was born in the night or female can be determined by:

P(Female or born at night)=P(Female)+P(Born at night)P(Female and born at night)=223513+262513116513=223+262116513=369513

So, option (a)localid="1649753827533" 369513is correct.

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