Birthday paradox

How large must the group of people be so that the probability that two people have a birthday on the same day of the year is greater than 90%?

Correct answer:

n =  41

Step-by-step explanation:

p1=13650.0027  q2=1364365=13650.0027 q3=1(1q2) 363365=1(10.0027) 3633650.0082 q4=1(1q3) 362365=1(10.0082) 3623650.0164  q5=1(1q4) 3654365=1(10.0164) 36543650.0271 q6=1(1q5) 3655365=1(10.0271) 36553650.0405 q7=1(1q6) 3656365=1(10.0405) 36563650.0562 q8=1(1q7) 3657365=1(10.0562) 36573650.0743 q9=1(1q8) 3658365=1(10.0743) 36583650.0946 q10=1(1q9) 3659365=1(10.0946) 36593650.1169 q11=1(1q10) 36510365=1(10.1169) 365103650.1411 q12=1(1q11) 36511365=1(10.1411) 365113650.167 q13=1(1q12) 36512365=1(10.167) 365123650.1944 q14=1(1q13) 36513365=1(10.1944) 365133650.2231 q15=1(1q14) 36514365=1(10.2231) 365143650.2529 q16=1(1q15) 36515365=1(10.2529) 365153650.2836 q17=1(1q16) 36516365=1(10.2836) 365163650.315 q18=1(1q17) 36517365=1(10.315) 365173650.3469 q19=1(1q18) 36518365=1(10.3469) 365183650.3791 q20=1(1q19) 36519365=1(10.3791) 365193650.4114 q21=1(1q20) 36520365=1(10.4114) 365203650.4437 q22=1(1q21) 36521365=1(10.4437) 365213650.4757 q23=1(1q22) 36522365=1(10.4757) 365223650.5073 q24=1(1q23) 36523365=1(10.5073) 365233650.5383 q25=1(1q24) 36524365=1(10.5383) 365243650.5687 q26=1(1q25) 36525365=1(10.5687) 365253650.5982 q27=1(1q26) 36526365=1(10.5982) 365263650.6269 q28=1(1q27) 36527365=1(10.6269) 365273650.6545 q29=1(1q28) 36528365=1(10.6545) 365283650.681 q30=1(1q29) 36529365=1(10.681) 365293650.7063 q31=1(1q30) 36530365=1(10.7063) 365303650.7305 q32=1(1q31) 36531365=1(10.7305) 365313650.7533 q33=1(1q32) 36532365=1(10.7533) 365323650.775 q34=1(1q33) 36533365=1(10.775) 365333650.7953 q35=1(1q34) 36534365=1(10.7953) 365343650.8144 q36=1(1q35) 36535365=1(10.8144) 365353650.8322 q37=1(1q36) 36536365=1(10.8322) 365363650.8487 q38=1(1q37) 36537365=1(10.8487) 365373650.8641 q39=1(1q38) 36538365=1(10.8641) 365383650.8782 q40=1(1q39) 36539365=1(10.8782) 365393650.8912 q41=1(1q40) 36540365=1(10.8912) 365403650.9032 q42=1(1q41) 36541365=1(10.9032) 365413650.914 n=41



Did you find an error or inaccuracy? Feel free to write us. Thank you!






avatar




Tips to related online calculators
Our percentage calculator will help you quickly calculate various typical tasks with percentages.
Do you want to convert time units like minutes to seconds?
Would you like to compute count of combinations?

Related math problems and questions:

  • Alarm systems
    cars What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
  • Records
    binomial Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
  • Sick days
    flu In Canada, there are typically 261 working days per year. If there is a 4.9% chance that an employee takes a sick day. .. what is the probability an employee will use 17 OR MORE sick days in a year?
  • Mastering
    test The student masters the subject matter for the exam in Czech to 98%, from Math to 86% and from Economics to 71%. What is the probability that he will fail from Math and from others will succeed?
  • Percents from percent
    percent How much is 13% of 20% of 500 greater than 8% of 14% of 200?
  • Dice
    dices How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
  • Double probability
    dices2 The probability of success of the planned action is 60%. What is the probability that we will achieve success at least once if this action is repeated twice?
  • Probability - tickets
    zreby What is the probability when you have 25 tickets in 5000 that you not wins the first (one) prize?
  • The university
    family At a certain university, 25% of students are in the business faculty. Of the students in the business faculty, 66% are males. However, only 52% of all students at the university are male. a. What is the probability that a student selected at random in the
  • Two doctors
    dr_cvach Doctor A will determine the correct diagnosis with a probability of 93% and doctor B with a probability of 79%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.
  • Doctors
    doktori The drug successfully treats 90% of cases. Calculate the probability that he will cure at least 18 patients out of 20?
  • Lathe
    sustruh 95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
  • Geography tests
    test On three 150-point geography tests, you earned grades of 88%, 94%, and 90%. The final test is worth 250 points. What percent do you need on the final to earn 93% of the total points on all tests?
  • Three shooters
    terc2 Three shooters shoot, each one time, on the same target. The first hit the target with a probability of 0.7; second with a probability of 0.8 and a third with a probability of 0.9. What is the probability to hit the target: a) just once b) at least once c
  • Utopia Island
    doktori The probability of disease A on the island of Utopia is 40%. The probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women o
  • Sales
    tesco From statistics of sales goods, item A buy 51% of people and item B buys 59% of people. What is the probability that from 10 people buy 2 item A and 8 item B?
  • Raffle
    tombola There are 200 draws in the raffle, but only 20 of them win. What is the probability of at least 4 winnings for a group of people who have bought 5 tickets together?