Question

If 3 people are asked what day of the week they were born, find the probability that
i) 2 or 3 are the same.

ii) only 2 people are the same.
- is this 1/7 x 1/7 ??

If 4 people are asked what day of the week they were born, what is the probability that 2 or more people were born on the same day.
- How do I show this??

Using this idea, work out how many people need to be asked for their birthdate so that at least two people sharing their birthdate will have a chance of 1/2.

Thank you

Answer 1

i) It is the proportion below for 2 the same, plus 1/7*1/7*1/7 for 3 the same. (Either-or probabilities are determined by adding the separate probabilities.)

ii) It is 1/7*1/7*6/7, because the third person has a different day of the week.

iii) Work the same as i) above, for 2, 3 <I>or</I> 4 sharing the same day.

The only way I know to find out is to expand iii) above to larger numbers until it equals 1/2.

I hope this helps.

Answer 2

Sorry, I was distracted by your attempt to answer ii). Your concern is for matching the first throw, whatever it is.

i) It is the proportion below for 2 the same, plus 1/7*1/7 for 3 the same. (Either-or probabilities are determined by adding the separate probabilities.)

ii) The first throw can be any number, so your concern is with matching that number, so ii) = 1/7*6/7.

iii) Work the same as i) above, for 2, 3 or 4 sharing the same day.

The only way I know to find out is to expand iii) above to larger numbers until it equals 1/2.