Probability

Initially there are 10 balls (6 white, 4 black). If one white ball is removed, 9 balls remain, 5 of which are white. The probability of drawing a white ball next is 5/9.

Primes between 1 and 52: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47. There are 15 primes. Probability = 15/52.

The sample space for two coins is {HH, HT, TH, TT}. Only one outcome (HH) is favorable. Probability = 1/4.

Total balls = 3 + 7 = 10. Number of blue balls = 3. Probability = 3/10.

The prime numbers on a standard die are 2, 3, and 5. Only 2 is an even prime number. The probability of rolling a 2 is 1/6.

A standard deck of playing cards contains 52 unique cards. Drawing one card from this deck results in 52 possible distinct outcomes.

A standard six-sided die has outcomes {1, 2, 3, 4, 5, 6}. Among these, the prime numbers are 2, 3, and 5. Note that 1 is not a prime number, and 4 and 6 are composite numbers.

The ordered pairs of dice outcomes whose sum is 8 are (2,6), (3,5), (4,4), (5,3), and (6,2). Thus, there are 5 outcomes.

The total outcomes when rolling two dice is 36. The outcomes that sum to 11 or 12 are (5,6), (6,5), and (6,6), which are 3 outcomes. The probability of getting 11 or 12 is 3/36 = 1/12, so the probability of getting 10 or lower is 1 - 1/12 = 11/12.

In a coin toss, there are two possible outcomes for any single toss: Head or Tail. The frequencies provided describe the results of 100 trials, but the number of possible outcomes remains two.

A standard 52-card deck contains 4 aces. The probability of drawing an ace is therefore 4/52, which simplifies to 1/13.

There is only one 10 of diamonds in a standard deck of 52 cards. Therefore, the probability is 1/52.

Total marbles = 20. Blue marbles = 10. Non-blue marbles = 20 - 10 = 10. The probability of not drawing a blue marble is 10/20 = 1/2.

A fair die has 6 faces. The probability of rolling a specific number (5) is 1 favorable outcome divided by 6 total possible outcomes.

The sample space for tossing a coin twice is {HH, HT, TH, TT}. There are 4 equally likely outcomes. Only one outcome is {TT}. Thus, the probability is 1/4.