You roll two (6-sided) number cubes, a red one and a white one. Find each probability:
a. P (5,2)
b. P (5, odd #)
c. P (3,3)
d. P (even #, odd #)
e. P (4,4)
f. P (less than five, 6)
To find the probability of an event, you need to determine the number of favorable outcomes (outcomes that satisfy the given condition) and the number of possible outcomes (total outcomes).
In this case, both dice are 6-sided, so each die has 6 possible outcomes (numbers 1 to 6).
a. P(5,2):
The event is getting a 5 on the red die and a 2 on the white die. There is only one favorable outcome - (5,2). The total number of outcomes is 6*6 = 36. Therefore,
P(5,2) = Number of favorable outcomes / Total number of outcomes = 1/36.
b. P(5, odd #):
The event is getting a 5 on the red die and an odd number on the white die. The favorable outcomes for the red die are just one - 5. The favorable outcomes for the white die are 1, 3, or 5. So, the number of favorable outcomes is 1 (red die) * 3 (white die) = 3. The total number of outcomes is still 6*6 = 36. Therefore,
P(5, odd #) = Number of favorable outcomes / Total number of outcomes = 3/36 = 1/12.
c. P(3,3):
The event is getting a 3 on both the red and white die. There is only one favorable outcome - (3,3). The total number of outcomes is 6*6 = 36. Therefore,
P(3,3) = Number of favorable outcomes / Total number of outcomes = 1/36.
d. P(even #, odd #):
The event is getting an even number on the red die and an odd number on the white die. The favorable outcomes for the red die are 2, 4, or 6. The favorable outcomes for the white die are 1, 3, or 5. So, the number of favorable outcomes is 3 (red die) * 3 (white die) = 9. The total number of outcomes is still 6*6 = 36. Therefore,
P(even #, odd #) = Number of favorable outcomes / Total number of outcomes = 9/36 = 1/4.
e. P(4,4):
The event is getting a 4 on both the red and white die. There is only one favorable outcome - (4,4). The total number of outcomes is 6*6 = 36. Therefore,
P(4,4) = Number of favorable outcomes / Total number of outcomes = 1/36.
f. P(less than five, 6):
The event is getting a number less than five on the red die and a 6 on the white die. The favorable outcomes for the red die are 1, 2, 3, or 4. The favorable outcome for the white die is 6. So, the number of favorable outcomes is 4 (red die) * 1 (white die) = 4. The total number of outcomes is still 6*6 = 36. Therefore,
P(less than five, 6) = Number of favorable outcomes / Total number of outcomes = 4/36 = 1/9.