1.A boy has 5 vests and 3 jackets. How many outfits can he wear if he wears both a vest and a jacket?How many outfits can he wear if he wears either a vest or a jacket?
2.If you roll two sided dice what is the probability of getting a 9? What is the probability of getting a different number on each die? what is the probability that the red die has higher number than the white die?
1. 5!3!
5! + 3!
2. two sided dice, wondering if 9 is on one face, two faces, or none.
Sorry i meant to say six sided dice
1. To find the number of outfits the boy can wear if he wears both a vest and a jacket, we can use the multiplication principle. Since he has 5 vests and 3 jackets, he can choose any one vest out of the 5 options and pair it with any one jacket out of the 3 options. This gives us a total of 5 * 3 = 15 different outfits.
To find the number of outfits the boy can wear if he wears either a vest or a jacket, we can use the addition principle. He can either wear a vest (choosing any one out of the 5 options) or a jacket (choosing any one out of the 3 options). Therefore, the total number of outfits would be 5 + 3 = 8.
2. If you roll two six-sided dice, the sum of the numbers on both dice can never be 9. The maximum sum you can get is 6 + 6 = 12. Therefore, the probability of getting a sum of 9 on two six-sided dice is 0.
To find the probability of getting a different number on each die, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes. There are 6 choices for the number on the first die and 5 choices for the number on the second die (since it can't be the same as the first die). Therefore, the total number of outcomes is 6 * 5 = 30 (since each choice on the first die can be paired with any of the 5 choices on the second die). The number of favorable outcomes is 30 (since all the outcomes have different numbers on each die). Therefore, the probability of getting a different number on each die is 30/30 = 1.
To find the probability that the red die has a higher number than the white die, we need to consider the possible outcomes. There are 6 choices for the number on each die. If we list all the possible outcomes, we see that there are 15 outcomes where the red die has a higher number than the white die. Therefore, the probability of the red die having a higher number is 15/36 = 5/12.