Question

National Statistics Day

a. If a person is randomly selected, find the probability that his or her birthday is October 18, which is National Statistics Day in Japan. Ignore leap years.

b. If a person is randomly selected, find the probability that his or her birthday is in October. Ignore leap years.

c. Estimate a subjective probability for the event of randomly selecting an adult American and getting someone who knows that October 18 is National Statistics Day in Japan.

d. Is it unlikely to randomly select an adult American and get someone who knows that October 18 is National Statistics Day in Japan?

Short answer

a. The probability of having a birthday on October 18 is $\frac{1}{365}$.

b. The probability that the randomly selected person celebrates his/her birthday in October is $\frac{31}{365}$.

c. The subjective probability is quite less (lesser than 0.01).

d. Yes, the event is unlikely.

Step-by-step solution

Define probability

A measure used to determine the occurence possibility of events is identified as probability. The measure is computed as quotient of two counts; favorable and total.

Mathematically, it is given as:

$P\left(A\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Total}\text{number}\text{of}\text{outcomes}}$

Compute the probability of having birthday on October 18

a.

The total number of days in a year is 365.

The number of days on which the randomly selected person can be born is 1; October 18.

The probability of event E, i.e.,the person was born on October 18 is:

$P\left(E\right)=\frac{1}{365}$

Thus, the probability that the randomly selected person has birthday on October 18 is$\frac{1}{365}$.

Compute the probability of the birthday being in October

b.

The total number of days in a year is 365.

The number of days on which the randomly selected person can be born is 31.

The probability of event F, i.e., the person was born in October is:

$P\left(F\right)=\frac{31}{365}$

Thus, the probability that the randomly selected person has birthday in October is$\frac{31}{365}$.

Estimate using subjective probability

c.

Subjective probability is the estimate of probability computed using information from personal judgment.

As the population of US adults is large, the total number of outcomes becomes large. Consequently, the probability of finding an American adult who knows that October 18 is National Statistics Day in Japan is small.

It can be estimated that the probability would be less than or equal to 0.01.

Interpret the result

d.

An unusual event is one that occurs with a probability less than or equal to 0.05. As the subjective estimate is lesser than 0.01, the event is unlikely to occur.

Thus, there are fewerchances that a randomly selected American would know October 18 as the National Statistics Day in japan.