Question

Exclude leap years from the following calculations. (a) Compute the probability that a randomly selected person does not have a birthday on October 3. (b) Compute the probability that a randomly selected person does not have a birthday on the 4th day of a month. (c) Compute the probability that a randomly selected person does not have a birthday on the 31st day of a month (d) Compute the probability that a randomly selected person was not born in March. (a) The probability that a randomly selected person does not have a birthday on October 3 is (Type an integer or a simplified fraction.) (b) The probability that a randomly selected person does not have a birthday on the 4th day of a month is (Type an integer or a simplified fraction.) (c)The probability that a randomly selected person does not have a birthday on the 31st day of a month is □ (Type an integer or a simplified fraction.) (d) The probability that a randomly selected person was not born in March is □ (Type an integer or a simplified fraction.) Enter your answer in each of the answer boxes.

Answer 1

Answer:

a) $\frac{364}{365}$

b) $\frac{353}{365}$

c) $\frac{358}{365}$

d) $\frac{334}{365}$

Step-by-step explanation:

(a) Compute the probability that a randomly selected person does not have a birthday on October 3

if p = Probability that a randomly selected person has a birthday on October 3, then

the probability that a randomly selected person does not have a birthday on October 3 = 1-p

There are 365 days in a year, therefore p=$\frac{1}{365}$

then 1-p= $\frac{364}{365}$

(b) Compute the probability that a randomly selected person does not have a birthday on the 4th day of a month.

similarly, if p = Probability that a randomly selected person has a birthday on the 4th day of a month, then

Probability that a randomly selected person does not have a birthday on the 4th day of a month is 1-p

Since a year has 12 months,

p = $\frac{12}{365}$

1-p= $\frac{353}{365}$

(c) Compute the probability that a randomly selected person does not have a birthday on the 31st day of a month

p=probability that a randomly selected person has a birthday on the 31st day of a month

1-p =probability that a randomly selected person does not have a birthday on the 31st day of a month

Since a year has 7 months having 31 day,

p= $\frac{7}{365}$

1-p=$\frac{358}{365}$

(d) Compute the probability that a randomly selected person was not born in March

p= the probability that a randomly selected person was born in March

1-p = the probability that a randomly selected person was not born in March

Since March has 31 days,

p= $\frac{31}{365}$

1-p=$\frac{334}{365}$