Question

select the correct answer from each drop - down menu.

hemoglobin level	age - less than 25 years	age - 25 - 35 years	age - above 35 years	age - total
between 9 and 11	49	52	46	147
above 11	69	44	40	153
total	139	128	162	429

based on the data in the two - way table, the probability of being 25 - 35 years old given a hemoglobin level above 11 is checkmark. the probability of being 25 - 35 years old is +. being 25 - 35 years old and having a hemoglobin level above 11 + dependent on each other.
options (for relevant blanks): 0.29, 0.34, 0.54
(buttons: reset, next)

Explanation:

Step1: Find conditional probability

We calculate the probability of being 25-35 years old given hemoglobin >11. Use the formula for conditional probability: $P(A|B)=\frac{P(A\cap B)}{P(B)}$. Here, $A$ is "25-35 years old", $B$ is "hemoglobin above 11".
$\frac{44}{153} \approx 0.29$

Step2: Find marginal probability

Calculate the probability of being 25-35 years old, using total counts.
$\frac{128}{429} \approx 0.30$ (closest to 0.29? No, wait, $\frac{128}{429}\approx0.30$, but the options have 0.34? Wait no, $\frac{128}{429}\approx0.30$, but wait, no, wait the options are 0.29, 0.34, 0.54. Wait, $\frac{128}{429}\approx0.30$, but the closest is 0.29? No, wait no, wait $\frac{128}{429}\approx0.30$, but maybe I miscalculated. Wait 4290.3=128.7, which is almost 128, so 0.30, but the options have 0.29, 0.34, 0.54. Wait, no, wait the first probability is $\frac{44}{153}\approx0.29$, correct. The second probability is $\frac{128}{429}\approx0.30$, but the closest option is 0.29? No, wait 4290.34=145.86, which is not 128. Wait 429*0.29=124.41, which is close to 128. Oh, maybe rounding. $\frac{128}{429}\approx0.298$, which rounds to 0.30, but the closest option is 0.29.

Step3: Check dependence

If $P(A|B)
eq P(A)$, then they are dependent. Here, $0.29
eq 0.30$, so they are dependent.

Answer:

1. The probability of being 25-35 years old given a hemoglobin level above 11 is 0.29
2. The probability of being 25-35 years old is 0.29
3. Being 25-35 years old and having a hemoglobin level above 11 are dependent on each other.

Wait, no, wait the second probability: $\frac{128}{429}\approx0.298$, which is approximately 0.30, but the options have 0.29, 0.34, 0.54. 0.29 is the closest. And since $P(A|B)=0.29$ and $P(A)\approx0.298\approx0.30$, which is not equal, so they are dependent.

Wait, no, wait maybe I made a mistake. Let's recalculate:
First probability: number of 25-35 with hemoglobin above 11 is 44, total with hemoglobin above 11 is 153. $\frac{44}{153}\approx0.2876\approx0.29$, correct.
Second probability: number of 25-35 is 128, total is 429. $\frac{128}{429}\approx0.2983\approx0.30$, but the options have 0.29, which is the closest.
Third: since $P(A|B)\approx0.29$ and $P(A)\approx0.30$, they are not equal, so the events are dependent.

Wait, but maybe the second probability is 0.34? No, $\frac{128}{429}\approx0.298$, which is not 0.34. 0.34429=145.86, which is not 128. 0.54429=231.66, which is way higher. So the second probability is approximately 0.29.

So the final answers are:

1. 0.29
2. 0.29
3. are

Wait, no, the third blank is "dependent on each other", so the word is "are".

Wait, let's confirm dependence:
If $P(A|B) = P(A)$, then independent. Here, $0.29
eq 0.298$, so they are dependent. So the third statement is "Being 25-35 years old and having a hemoglobin level above 11 are dependent on each other."

Yes.

So the final answers:

1. 0.29
2. 0.29
3. are