Q: What is the probability that a randomly chosen month has 30 days?

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The probability is approx 15/16.

Just over 7 out of 12.

The probability of an event is one when the event is absolutely certain to happen. It is more useful to understand why the sum of probabilities of an event adds up to one. If you have an event with a probability of p, then the probability of the event not occurring is 1 - p. This is because p plus (1 - p) is 1. That seems trivial, but consider a realistic example... Lets say you are subject to random drug testing, and that you are in a 100% pool such as might be mandated by 10CFR26, "Fitness for Duty in a Commericial Nuclear Power Plant". What is the probability that you will be chosen at least once in a year? Well, if sampling occurs five days a week, then there are 260 samples per year. The probability of being chosen in one sample is 1 in 260, or 0.003846. That means the probability of not being chosen is 259 in 260, or 0.9962. The probability, then, of not being chosen in one year is (259 in 260) raised to the 260th power, or 0.3672, which is about 95 in 260. Invert once again, and you see that the probability of being chosen at least one time in a year is 165 in 260, or 0.6328.

If the probability that it will rain is 0.25, then the probability that it is sunny is 0.75. The probability of it being sunny for five days, then is 0.755, or about 0.2373.

February 29 occurs 97 times in 400 years (not once in 4 years). Therefore, there are 97 favourable events out of 146,097 days which gives a probability of 0.00066 approx. However, this assumes that birthdays are randomly spread over the course of a year. This is certainly not true, and February is "low season" for births so the true probability will be lower.

Related questions

There are 12 months to choose from There are 7 months with 31 days in them. The probability of choosing a 31-day month is 7/12.

The probability is 7:12... There are five months with less than 31 days, so the probability of selecting a month with exactly 31 days is 7 out of 12.

First we don't consider leap year There is 1 month with 28 days: february There are 4 months with 30 days: april, june, september, november So the probability to select a month with 28 or 30 days is (1+4)/12 = 5/12 If the year is a leap year then the probability is 4/12

It is 1. Every month contains 28 days.

It is 7/12.

The probability is approx 15/16.

Feb was the most famous month with 29 days

Absolute certainty

you wont get your birthday every year

Just over 7 out of 12.

Let us assume that there are exactly 365 days in a year and that birthdays are uniformly randomly distributed across those days. First, what is the probability that 2 randomly selected people have different birthdays? The second person's birthday can be any day except the first person's, so the probability is 364/365. What is the probability that 3 people will all have different birthdays? We already know that there is a 364/365 chance that the first two will have different birthdays. The third person must have a birthday that is different from the first two: the probability of this happening is 363/365. We need to multiply the probabilities since the events are independent; the answer for 3 people is thus 364/365 × 363/365. You should now be able to solve it for 4 people.

It depends what you mean by randomly. If its not eaten anything for one or two days - but regains its appetite, I wouldn't worry. However - if it's been more than a couple of days - take it to a vet for a check up !