Jennifer writes the letters M-O-N-T-A-N-A on cards and then places the cards in a hat. What are the odds in favor of picking a vowel?
3:7
4:7
3:4
4:3
I think its 3:7
And my other question is..
Jennifer writes the letters M-O-N-T-A-N-A on cards and then places the cards in a hat. What are the odds against picking a vowel?
3:7
4:7
3:4
4:3
My answer: 4:7
Both are wrong
Odds and probability are not the same thing
you have found the prob(picking a vowel)
Odds in favour of picking a vowel
= prob of picking a vowel : prob of NOT picking a vowel
= 3/7 : 4/7
= 3 : 4
the second question simply reverses the odds
should be
4 : 3
Both are correct.
You are correct. The odds in favor of picking a vowel are 3:7, meaning there are 3 favorable outcomes (vowels) out of a total of 7 possible outcomes (all the letters).
For the odds against picking a vowel, you are also correct. The odds against picking a vowel are 4:7, meaning there are 4 unfavorable outcomes (non-vowels) out of a total of 7 possible outcomes (all the letters).
To determine the odds in favor of or against picking a vowel, we need to count the number of vowels and the total number of cards in the hat.
1. Counting vowels:
In the word "M-O-N-T-A-N-A," the vowels are A and O. So, there are 2 vowels.
2. Counting total cards:
The word "M-O-N-T-A-N-A" contains 7 letters. Therefore, there are 7 cards in total.
3. Odds in favor of picking a vowel:
The odds in favor of picking a vowel is the ratio of the number of desired outcomes (picking a vowel) to the number of possible outcomes (total cards). In this case, the desired outcomes are picking a vowel (2) and the total outcomes are the total number of cards (7). So the odds in favor are 2:7.
Therefore, your answer of 3:7 is not correct.
4. Odds against picking a vowel:
The odds against picking a vowel is the ratio of the number of unfavorable outcomes (not picking a vowel) to the number of possible outcomes (total cards). In this case, the unfavorable outcomes are not picking a vowel, which is equal to the total number of cards (7) minus the number of vowels (2) which is 5. So the odds against picking a vowel are 5:7.
Therefore, your answer of 4:7 for the odds against picking a vowel is correct.