These are 2 problems that I'm stuck on; I know the answers to them but I just don't know how to find that answer. Can someone please help?
1. The probability that the Lions football team will win the next game is 0.6. What are the odds that it'll win?
Ans- Odds in favor of the team are 3 to 2
2.Two game cubes are rolled. Find the odds against obtaining the number 7.
Ans- Odds against obtaining the sum of 7 are 5 to 1.
Thanks
-MC
1. the probability is the good divided by the total; the odds are the good divided by the bad.
if the good is 0.6, the bad is (1-0.6)=0.4. 0.6/0.4 = 3/2
2. Find the total number of possibilities. Each die has 6 sides, so the total is 6*6 = 36.
Now, find the number of ways you can get 7. 1+6, 2+5, 3+4, 4+3, 5+2, 6+1. 6 ways.
Find the bad: 36-6 = 30.
If you're finding odds against, divide the bad by the good: 30/6 = 5/1
If the probability is .6, that is 6/10 or 3/5 which means it should win 3 of five games, and lose 2 games. Odds win:lose are 3:2
On the second: how many ways can you get seven? (6,1, 1,6, 3,4, 4,3 , 2,5; 5,2m ) or six ways out of 36 ways to throw the dice. There are six ways to get seven, 30 ways to not get it. That is five to one for not getting it.
Of course, I'd be happy to help explain how to find the answers to these problems.
1. To find the odds that the Lions football team will win, you first need to understand what the probability of winning is. In this case, the probability is given as 0.6. The probability can be written as P(Event) = Number of favorable outcomes / Total number of possible outcomes.
Now, let's define the odds in favor of an event as the ratio P(Event) / (1 - P(Event)). In this case, the odds in favor of the Lions winning would be 0.6 / (1 - 0.6) = 0.6 / 0.4.
To simplify, we can convert this ratio into a fraction. In this case, 0.6 / 0.4 can be simplified to 3/2. Therefore, the odds in favor of the Lions winning the next game are 3 to 2.
2. To find the odds against obtaining the number 7 when two game cubes are rolled, we need to understand the probability of obtaining a sum of 7. In this case, we need to calculate the probability of getting a sum of 7.
There are 6 possible outcomes when rolling a die (numbers 1 to 6), and each die has 6 sides. So, the total number of possible outcomes is 6 * 6 = 36.
Out of these 36 outcomes, there are 6 possible ways to obtain a sum of 7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6,1).
Hence, the probability of obtaining a sum of 7 is 6/36, which simplifies to 1/6.
Now, let's calculate the odds against obtaining the sum of 7. The odds against an event is given as (1 - P(Event)) / P(Event). In this case, it would be (1 - 1/6) / (1/6).
To simplify, we can convert this into a fraction. (1 - 1/6) / (1/6) can be simplified to 5/1. Therefore, the odds against obtaining the sum of 7 when rolling two game cubes are 5 to 1.
I hope this explanation helps you understand how to find the answers to these problems. Let me know if you have any further questions!