Karen claims that the odds against randomly drawing the letter S from the letters in the word MISSISSIPPI are 4:7. How do you respond?
The ratio is 4:7, but the odds are 4/11, # Ss vs the total possible choices.
prob of drawing an S = 4/11
prob of NOT drawing an S = 1 - 4/11 = 7/11
So the odds in favour of drawing an S
= (4/11) : (7/11)
= 4 : 7
So the odds AGAINST drawing an S = 3 : 7
I would say, "Karen, read the question carefully"
Argghhh!
the odds AGAINST drawing an S = 7 : 3
To determine if the odds against randomly drawing the letter S from the letters in the word MISSISSIPPI are indeed 4:7, we need to calculate the probability of drawing the letter S and compare it to the probability of not drawing the letter S.
Step 1: Count the total number of letters in the word MISSISSIPPI.
There are a total of 11 letters in the word MISSISSIPPI.
Step 2: Count the number of occurrences of the letter S in the word MISSISSIPPI.
There are 4 occurrences of the letter S in the word MISSISSIPPI.
Step 3: Calculate the probability of drawing the letter S.
The probability of drawing the letter S is given by the formula: Probability of an event = Number of favorable outcomes / Total number of outcomes.
In this case, the number of favorable outcomes is 4 (the number of occurrences of the letter S), and the total number of outcomes is 11 (the total number of letters in the word).
So, the probability of drawing the letter S is 4/11.
Step 4: Calculate the probability of not drawing the letter S.
The probability of not drawing the letter S is 1 minus the probability of drawing the letter S.
So, the probability of not drawing the letter S is 1 - (4/11), which simplifies to 7/11.
Step 5: Check if the calculated probabilities match the odds given by Karen (4:7).
The odds against drawing the letter S are expressed as a ratio of unfavorable outcomes to favorable outcomes. In this case, the ratio is 4:7.
Comparing the calculated probabilities, we see that the probability of drawing the letter S is 4/11, which does not match the given ratio of 4:7.
Therefore, we can conclude that Karen's claim about the odds against randomly drawing the letter S from the word MISSISSIPPI is incorrect.