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What is the probability that the birthdays of five persons chosen at random will fall in twelve different calendar months?
The probability that the birthdays of five persons chosen at random will fall in twelve different calender months is zero. You would need at least twelve persons to have a non zero probability.
What is the probability that your birthday will fall on Saturday or Sunday?
2/7, as there 7 days in a week.
What is the probability of at least one birthday match among a group of 41 people?
The probability of at least 1 match is equivalent to 1 minus the probability of there being no matches. The first person's birthday can fall on any day without a match, so the probability of no matches in a group of 1 is 365/365 = 1. The second person's birthday must also fall on a free day, the probability of which is 364/365 The probability of the third person also falling on a free day is 363/365, which we must multiply by the probability of the second person's birthday being free as this must also happen. So for a group of 3 the probability of no clashes is (363*364)/(365*365). Continuing this way, the probability of no matches in a group of 41 is (365*364*363*...326*325)/36541 This can also be written 365!/(324!*36541) Which comes to 0.09685... Therefore the probability of at least one match is 1 - 0.09685 = 0.9032 So the probability of at least one match is roughly 90%
If 5 distinct dice are rolled what is the probability of getting at least one 6?
You must notice that it is easier to find the probability that none of the dice are six. This is the complement of the answer. Pc= (55)/(65) = .4019 *the first die has 5 ways to not equal six, and so on for the remaining dice. [55] outcomes have no six. *the total number of outcomes gives each die 6 ways to fall. [65] outcomes overall. *Probability is the favorable outcome divided by the total number of outcomes. *Probability of an event is 1 minus the complement of the event. P = 1 - .4019 P = .5981 <<<<<<FINAL ANSWER
What is the probability that your birthday this year will not fall on a day of the week that begins with the letter T?
It is 1, since it falls on a Wednesday.
