Records from a dairy farm yielded the following information 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 probability that a randomly selected calf was born in the night or was a female is369513.

Step by step solution

01

Given information

The table is

Time of day

Gender


Dayeveningnighttotal
Males12915117261
Females11818116252
Total24733233513

Formulae used:

Probability=Fawourable CasesTotal Cases

Complement rule:

PAc=P(notA)=1-P(A)

Addition rule for any two events:

P(AorB)=P(A)+P(B)-P(AandB)

Definition conditional probability:

P(B/A)=P(AB)P(A)=P(AandB)P(A)
02

Explanation for correct option

It has been discovered that 233 of the 513 people were born at night.

P(Born at night)=Noof favorable outcomesNoof possible outcomes=233513

It was also discovered that 252 of the 513 people were female.

P(Female)=Noof favorable outcomesNoof possible outcomes=252513

Finally, we should mention that 116 of the 513 people were female and were born at night.

P (Female and Born at night)=Noof faworable outcomesNoof possible outcomes=116513

P( Female and Born at night)=P (Female) +P (Born at night) -P

(Female and Born at night)

=233513+252513-216513=223-262-116513=369513

Therefore, the correct option is (a)

03

Explanation for incorrect option

(b) The probability that a randomly selected calf was born in the night or was a female is not485513

(c) The probability that a randomly selected calf was born in the night or was a female is not116513

(d) The probability that a randomly selected calf was born in the night or was a female is not 116252

(e) The probability that a randomly selected calf was born in the night or was a female is not 116233

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