100 keys are in a bucket. 61 of them are gold. what is the probability of drawing 2 gold keys if the first…

Answer:

0.37

Explanation:

Step1: Calculate probability of first draw

The probability of drawing a gold - key on the first draw is the number of gold keys divided by the total number of keys. There are 61 gold keys and 100 total keys, so $P_1=\frac{61}{100}=0.61$.

Step2: Calculate probability of second draw

Since the first key is placed back, the situation for the second draw is the same as the first. So the probability of drawing a gold key on the second draw is also $P_2 = \frac{61}{100}=0.61$.

Step3: Calculate probability of both events

Since the two draws are independent events, the probability of both drawing gold keys is the product of the probabilities of each draw. So $P = P_1\times P_2=0.61\times0.61 = 0.3721$. Rounding to the nearest hundredth gives 0.37.