1. a. The probability of getting a heart is 13/52 which reduces to 1/4.
b. The probability of getting a face card is 12/52 which reduces to 3/4.
2. a. There are 12 blue marbles and a total of 28 marbles in a jar. The probability that first marble selected is blue is 12/28. The probability of the second marble is still blue is 11/27. To get the probability of selecting two blue marbles at random, we will just multiply the two probabilities which gives us 132/756 which reduces to 11/63. Therefore the probability of selecting a blue marble is 11/63.
b. The probability of the first marble that is not green is 12/28. The probability of the second marble which is still not green is 11/27. We will just multiply the two probabilities to get the probability of selecting a marble which is not green which is 462/756 which reduces to 11/18.
3. There are 5 prime numbers from 1-9 and there are total of 9 numbers from 1-9.
The probability of getting the first number is 5/9, second number is 4/8, third number is 3/7. We will multiply the three probabilities, which gives us product of 60/504 which reduces to 5/42. Therefore the probability of selecting a 3-digit number is 5/42.