Answer:
Step-by-step eTo solve this problem, we first need to find the probability of pulling an orange block, then the probability of pulling another orange block consecutively.
1. Probability of pulling an orange block:
There are a total of \(3 + 5 + 4 = 12\) blocks in the bag.
The probability of pulling an orange block on the first draw is \(P(\text{orange}) = \frac{3}{12} = \frac{1}{4}\).
2. Probability of pulling another orange block consecutively:
After pulling one orange block, there are \(12 - 1 = 11\) blocks left in the bag.
Since we didn't replace the first orange block, there are now only \(3 - 1 = 2\) orange blocks left in the bag.
So, the probability of pulling another orange block consecutively is \(P(\text{orange}) = \frac{2}{11}\).
To find the probability of both events happening consecutively, we multiply the probabilities:
\[ P(\text{consecutive oranges}) = P(\text{orange on first draw}) \times P(\text{orange on second draw}) \]
\[ P(\text{consecutive oranges}) = \frac{1}{4} \times \frac{2}{11} \]
\[ P(\text{consecutive oranges}) = \frac{1}{4} \times \frac{2}{11} = \frac{1 \times 2}{4 \times 11} = \frac{2}{44} = \frac{1}{22} \]
So, the probability of consecutively pulling two more orange blocks, without replacement, from those that remain in the bag is \( \frac{1}{22} \).xplanation: