In a large vase, there are 8 roses, 5 daisies, 12 lilies and 9 orchids. If 3 flowers are selected at random, find the probability that at least 1 of the flowers is a lily.
Assuming that the events are dependent. Would you consider this event likely to
occur? Explain your answer.
Can someone show me the calculation. the ans is 0.7426
what is the chance that no flower is a lily?
22/34 * 21/33 * 20/32 = 0.2574
Now subtract that from 1 and you have your answer
To find the probability that at least one of the flowers selected is a lily, we need to calculate the probability of the complement event (where none of the flowers selected is a lily) and subtract it from 1.
The total number of flowers in the vase is 8 + 5 + 12 + 9 = 34.
Calculating the probability of selecting 3 flowers without any lilies:
Probability of selecting a non-lily flower on the first draw = (total non-lily flowers) / (total flowers) = (8 + 5 + 9) / 34 = 22 / 34 = 11 / 17.
Probability of selecting a non-lily flower on the second draw = (total non-lily flowers - 1) / (total flowers - 1) = (22 - 1) / (34 - 1) = 21 / 33.
Probability of selecting a non-lily flower on the third draw = (total non-lily flowers - 2) / (total flowers - 2) = (22 - 2) / (34 - 2) = 20 / 32 = 5 / 8.
Now, multiply the probabilities together to find the probability of not selecting any lilies: (11/17) * (21/33) * (5/8) = 385/1122 ≈ 0.3436.
Finally, subtract this value from 1 to find the probability of at least one lily: 1 - 0.3436 ≈ 0.6564.
Therefore, the probability of at least one of the flowers being a lily is approximately 0.6564.
As for whether this event is considered likely, it ultimately depends on the specific context and the perspective of the person assessing the likelihood. In this case, the probability is greater than 0.5, indicating that it is more likely than not that at least one of the flowers selected will be a lily.
To find the probability that at least 1 of the flowers selected is a lily, we can use the concept of complementary probability. We calculate the probability that none of the flowers selected is a lily and subtract it from 1.
First, let's calculate the probability that none of the flowers selected is a lily:
Step 1: Find the total number of flowers in the vase:
Total number of flowers = 8 roses + 5 daisies + 12 lilies + 9 orchids = 34
Step 2: Find the number of ways to select 3 flowers from the total:
Number of ways to choose 3 flowers = C(34, 3) = 34! / (3! * (34 - 3)!) = 5,244
Step 3: Find the number of ways to choose 3 flowers without any lilies:
Number of ways to choose 3 non-lily flowers = C(22, 3) = 22! / (3! * (22 - 3)!) = 1,540
Step 4: Calculate the probability of selecting 3 non-lily flowers:
Probability of selecting 3 non-lily flowers = 1,540 / 5,244 ≈ 0.2936
Step 5: Find the complementary probability (probability of at least 1 lily):
Probability of at least 1 lily = 1 - 0.2936 ≈ 0.7064
Therefore, the probability that at least 1 of the flowers selected is a lily is approximately 0.7064 or 70.64%.
As for whether this event is likely to occur, it depends on the context and individual perspective. With a probability of around 70.64%, one might consider it relatively probable that at least one of the flowers selected is a lily. However, the likelihood can vary depending on personal expectations and what is considered "likely" in the given context.