First, let's understand the given problem. Natasha is simulating the gender of four kittens by tossing a coin, where heads (H) represent female kittens and tails (T) represent male kittens. We need to estimate the probability that at least three of these kittens will be male.
Here are the results of Natasha's simulation, which consists of 10 different trials:
1. HHHT
2. HHHH
3. HHTH
4. THTH
5. THTT
6. TTHT
7. HHHT
8. TTHH
9. THHT
10. HTTT
Our goal is to determine how many of these trials result in at least three male kittens (i.e., at least three tails).
Let's go through each trial to count the number of trials with at least three male kittens:
1. HHHT: 1 male
2. HHHH: 0 males
3. HHTH: 1 male
4. THTH: 2 males
5. THTT: 3 males (at least 3, so this counts)
6. TTHT: 3 males (at least 3, so this counts)
7. HHHT: 1 male
8. TTHH: 2 males
9. THHT: 2 males
10. HTTT: 3 males (at least 3, so this counts)
We found 3 trials (trial 5, trial 6, and trial 10) where at least three kittens are male.
Next, let's calculate the probability. The total number of trials is 10.
The estimated probability [tex]\( P \)[/tex] that at least three of the kittens will be male is given by:
[tex]\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of trials}} = \frac{3}{10} \][/tex]
To convert this probability into a percentage:
[tex]\[ \text{Percentage} = P \times 100\% = 0.3 \times 100\% = 30\% \][/tex]
So the estimated probability that at least three of the kittens will be male is:
[tex]\[ \frac{3}{10} = 30\% \][/tex]
Hence, the correct answer is:
B. [tex]\(\frac{3}{10} = 30\%\)[/tex]
