Answer:
the probability that Yasmine takes at least one green counter is 0.368 or 36.8%.
Explanation:
To find the probability that Yasmine takes at least one green counter, you need to consider the total number of possible outcomes and the number of favorable outcomes.
The total number of counters in the bag is 4 (green) + 5 (red) + 11 (black) = 20 counters.
When Yasmine takes the first counter, there are 20 counters in the bag. Since she wants to take at least one green counter, there are two scenarios to consider:
1. Yasmine takes a green counter on her first draw.
In this case, there are 4 green counters out of 20 total counters. Therefore, the probability of Yasmine taking a green counter on her first draw is 4/20.
2. Yasmine does not take a green counter on her first draw.
In this scenario, there are now 19 counters left in the bag, with 4 green counters remaining. Therefore, the probability of Yasmine not taking a green counter on her first draw is (20-4)/20 = 16/20.
Now, for the second draw, you need to consider two possibilities:
a) If Yasmine took a green counter on her first draw:
In this case, there are now 3 green counters left out of the remaining 19 counters in the bag. Therefore, the probability of Yasmine taking a green counter on her second draw given that she took a green counter on her first draw is 3/19.
b) If Yasmine did not take a green counter on her first draw:
In this scenario, there are still 4 green counters left out of the remaining 19 counters in the bag. Therefore, the probability of Yasmine taking a green counter on her second draw given that she did not take a green counter on her first draw is 4/19.
To find the overall probability of Yasmine taking at least one green counter, you need to consider the two scenarios and their respective probabilities:
Scenario 1: Yasmine takes a green counter on her first draw (4/20) and any counter on her second draw (1).
Scenario 2: Yasmine does not take a green counter on her first draw (16/20), but takes a green counter on her second draw given that she did not take one on her first draw ((16/20) * (4/19)).
The overall probability is the sum of these two scenarios:
(4/20) + ((16/20) * (4/19)) = 0.2 + 0.168 = 0.368.
Therefore, the probability that Yasmine takes at least one green counter is 0.368 or 36.8%.