A hen laid exactly 6 eggs each week for 3 weeks of a 12 week period. The same hen also laid 4 eggs or fewer each week for 6 weeks during the same 12 week period.
Based on the data, what is the probability that the hen will lay exactly 6 eggs next week?
Responses
A
1 /4
B
1 /6
C
3/ 6
D 3/4
What is the chance that the hen will lay 4 eggs or fewer next week?
Responses
A 60% chance
B 50% chance
C 40% chance
D 25% chance
For the first question, we know that the hen laid exactly 6 eggs each week for 3 weeks out of 12, so the probability of her laying exactly 6 eggs in any given week is 3/12 or 1/4. Therefore, the answer is A) 1/4.
For the second question, we know that the hen laid 4 eggs or fewer each week for 6 weeks out of 12, so the probability of her laying 4 eggs or fewer in any given week is 6/12 or 1/2. Therefore, the answer is B) 50% chance.
Suppose that 1/2
of the children in preschool are scared of snakes, 1/3
are scared of spiders, and 1/12
are scared of snakes and spiders.
What fraction of those who are scared of spiders are also scared of snakes?
Responses
A
1/ 4
B
1/ 3
C
1/ 6
D 1/2
What fraction of those who are scared of snakes are also scared of spiders?
Responses
A
1 /2
B
1/ 3
C
1/ 6
D 1/4
To solve this problem, we can use conditional probability. We want to find the fraction of those who are scared of spiders that are also scared of snakes. Let S denote the event of being scared of snakes, and P denote the event of being scared of spiders. Then the probability of S given P is:
P(S|P) = P(S and P) / P(P)
We know that P(S and P) = 1/12, and P(P) = 1/3. To find P(S|P), we just need to substitute these values:
P(S|P) = (1/12) / (1/3) = 1/4
Therefore, the answer to the first question is A) 1/4.
Similarly, we want to find the fraction of those who are scared of snakes that are also scared of spiders. Using the same formula as before, we get:
P(P|S) = P(S and P) / P(S)
We know that P(S and P) = 1/12, and P(S) = 1/2. Substituting these values, we get:
P(P|S) = (1/12) / (1/2) = 1/6
Therefore, the answer to the second question is C) 1/6.
To calculate the probability of the hen laying exactly 6 eggs next week, we need to look at the given data. From the information provided, we know that the hen laid exactly 6 eggs each week for 3 weeks out of a 12 week period.
We can calculate the probability by dividing the number of favorable outcomes (weeks the hen laid exactly 6 eggs) by the total number of possible outcomes (12 weeks).
Therefore, the probability of the hen laying exactly 6 eggs next week is 3/12, which simplifies to 1/4.
So, the correct answer for the probability of the hen laying exactly 6 eggs next week is A) 1/4.
Now, let's calculate the probability of the hen laying 4 eggs or fewer next week. We know that for 6 weeks out of the 12 week period, the hen laid 4 eggs or fewer.
Similarly, we can calculate the probability by dividing the number of favorable outcomes (weeks the hen laid 4 eggs or fewer) by the total number of possible outcomes (12 weeks).
Therefore, the probability of the hen laying 4 eggs or fewer next week is 6/12, which simplifies to 1/2.
So, the correct answer for the probability of the hen laying 4 eggs or fewer next week is B) 50% chance.