Since every month except May, June, July and August has a R in its name, the odds of someone born in a month whose name contains an R is roughly 2/3. The exact number is closer to 66.32% (242.2425 ÷ 365.2425).
The probability of randomly choosing 1 blue sock is 7/10. The probability of randomly choosing 2 blue socks in a row is 7/10 x 7/10 = 49/100.
If you select 45 cards without replacement from a regular deck of playing cards, the probability is 1. For a single randomly selected card, the probability is 2/13.
If 10 out of 26 are girls, then the probability of randomly choosing a boy is 16 out of 26, or 8 out of 13, or about 0.6154.
In the sample space [1,20], there are 8 prime numbers, [2,3,5,7,11,13,17,19]. The probability, then, of randomly choosing a prime number in the sample space [1,20] is (8 in 20), or (2 in 5), or 0.4. The probability of choosing two of them is (8 in 20) times (7 in 19) which is (56 in 1064) or (7 in 133) or about 0.05263.
The theoretical probability of getting an odd product would depend on the specific scenario. If we are talking about rolling a pair of fair dice, the probability would be 1/2 since half of the possible outcomes (3, 5, 15, etc.) would result in an odd product. However, if we are talking about multiplying two randomly selected numbers from a large set, the probability would depend on the distribution of the numbers in the set.
There are five letters, and two of them are s's. The theoretical probability of choosing an s would be 2 out of 5.2/5 or 40%
The probability of randomly choosing 1 blue sock is 7/10. The probability of randomly choosing 2 blue socks in a row is 7/10 x 7/10 = 49/100.
Empirical
If you select 45 cards without replacement from a regular deck of playing cards, the probability is 1. For a single randomly selected card, the probability is 2/13.
The theoretical probability of randomly picking each color marble is the number of color marbles you have for each color, divided by the total number of marbles. For example, the probability of selecting a red marble is 3/20.
If 10 out of 26 are girls, then the probability of randomly choosing a boy is 16 out of 26, or 8 out of 13, or about 0.6154.
The probability of drawing a queen or king, in a single randomly drawn card, is 2/13. The probability of drawing one when you draw 45 cards without replacement is 1. The probability of choosing has nothing t do with the probability of drawing the card. I can choose a king but fail to find one!
The theoretical probability of randomly drawing a green marble can be calculated by dividing the number of green marbles by the total number of marbles in the bag. In this case, there are 12 green marbles out of a total of 5 red marbles + 8 blue marbles + 12 green marbles, which is 25 marbles in total. Therefore, the theoretical probability of drawing a green marble is 12/25 or 48%.
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.
It is 15/38.
There are 20 numbers from 20 through 39, and 4 of them are prime (23, 29, 31, 37), the probability is 4 in 20 or 0.20.
The answer depends on how refined the theory is. The simplest theory is that birthdays are distributed evenly through the year across the world. If that were the case, the answer is 1/2. However, anyone who has spent even a short time studying the subject will know that birthdays are not evenly distributed. The month to month variations, plus differences between countries need to be taken into account before a half-way decent theoretical model can be constructed.