01.If two regular six-sided dice are rolled at the same time, what is the probability that the sum of the their numbers will be prime?
Possible Answers:
5/12
1/2
1/4
7/18
5/12
There number of possible outcomes is equal to six times six, or thirty-six. The sum of the two dice must be either 2, 3, 5, 7, or 11. There are 15 out of the 36 outcomes that would result in a sum that is a prime number:
[1,1], [1,2], [1,4], [1,6], [2,1], [2,3], [2,5], [3,2], [3,4], [4,1], [4,3], [5,2], [5,6], [6,1], [6,5]
2.Maria is planning the seating for the head table at a college gala. There are eight speakers that will be seated along one side of the table. Richard wants to sit beside Hang, and Maria knows that Thomas and Lily should not be seated together. In how many ways can Maria make up the seating plan?
The simplest way to solve this is to find the number of seating arrangements in which Richard and Hang are seated together and then subtract those in which Thomas and Lily are also seated together. Consider Richard and Hang as a unit. This pair can be arranged with the other six speakers in 7P7 ways. For each of these ways, Hang could be either on Richard’s left or his right. Thus, there are 7P7 × 2 = 10 080 arrangements in which Richard and Hang are seated together. Now also consider Lily and Thomas as a unit. The two pairs can be arranged with the remaining four speakers in 6P6 ways, and the total number of arrangements with each of the pairs together is 6P6 × 2 × 2 = 2880.
Therefore, the number of seating arrangements in which Richard and Hang are adjacent but Thomas and Lily are not is 10 080 − 2880 = 7200
3.You roll a six sided die three times. What are the chances that all three rolls are 2?
1/216
1/6
1/18
1/36
1/12
1/216
Probability of each event = 1 side of die / # of sides = 1/6
Probability for multiple events = P1 * P2 * P3
1/6 x 1/6 x 1/6 = 1/216
4.What is the probability of NOT getting a 7 when rolling two standard six-sided dice?
1/6
1/4
2/3
1/3
5/6
5/6
The sample space for rolling two six-sided dice is 36. We can get 7 six different ways: 1,6 2,5 3,4 4,3 5,2 6,1 so the probability of getting a 7 is 636 or 16. The probability of NOT getting a 7 is 1−16=56. We can add up all the things we want or we can subtract from 1 what we don't want.
5.Jane bought 30 pens, 9 of which had black ink, 10 blue ink and 11 red ink. On the way home from the store all the pens got mixed together and 2 blue pens were lost. When Jane arrives home she reachs into the bag and randomly picks a pen. What are the chances she will pick a blue pen?
1/5
2/7
1/3
3/10
4/15
27
When Jane starts she has a total of 30 pens, 9 black, 10 blue and 11 red. Two of the blue pens were lost. This dropped the number of blue pens to 8 and the total count of pens to 28.
To find the probability of something happening, take the total amount of things in question, the blue pens or 8, and compare them to total amount of pens which is now 28 pens.
8 blue pens/28 total pens= 1/7 chance to draw a blue pen from the bag.
*The pitfall for these types of questions is to realize that not only does the count of blue pens decrease but also the total count of pens. Make sure to adjust both values.
