How do you find the odds if the probability of tossing a total of 7 two number cubes is 1/6.
There are 6x6= 36 possible outcomes of throwing 2 dice, if you keep track of each die (A & B) separately.
The combinations that result in 7 are:
A --B
-----
1 & 6
2 & 5
3 & 4
4 & 3
5 & 2
6 & 1
All outcomes are equally likely. That's 6 combinations that yield a sum of 7 out of 36, and that equals 1/6.
The ODDS in favour of an EVENT
= Prob(EVENT happening) : Prob(EVENT not happening)
prob(a seven) = 1/6
prob (not a seven) = 5/6
so the odds in favour of a seven = (1/6) : (5/6)
= 1:5
in the same way the odd against throwing a seven would be 5:1
To find the odds, you need to determine the probability of the event occurring and compare it to the probability of the event not occurring. In this case, let's first calculate the probability of tossing a total of 7 with two number cubes.
A standard six-sided die has 6 possible outcomes: 1, 2, 3, 4, 5, or 6. When you roll two dice, the total number of outcomes is the product of the number of outcomes on each die. In this case, each die has 6 possible outcomes, so the total number of outcomes when rolling two dice is 6 * 6 = 36.
Next, let's determine the number of outcomes that result in a total of 7. These outcomes can occur in different ways: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), or (6, 1). So, there are 6 outcomes that result in a total of 7.
Therefore, the probability of obtaining a total of 7 by rolling two number cubes is 6/36, which simplifies to 1/6.
To find the odds, we need to compare this probability to the probability of not getting a total of 7. The probability of not getting a total of 7 is equal to 1 - (probability of getting a total of 7). So, the probability of not getting a total of 7 is 1 - (1/6) = 5/6.
Finally, we can express the odds as a ratio of the probability of the event occurring to the probability of the event not occurring. Therefore, the odds of tossing a total of 7 with two number cubes is 1/6 : 5/6, or simply 1:5. This means that for every 1 successful outcome, there are 5 unsuccessful outcomes, giving you the odds of the event happening.