For a randomly selected day, the probability that a visitor to a certain pond will see at least one swan...
GMAT Two Part Analysis : (TPA) Questions
For a randomly selected day, the probability that a visitor to a certain pond will see at least one swan is 0.35. The probability that a visitor to that pond on a randomly selected day will see at least one heron is 0.2. Furthermore, seeing a swan and seeing a heron are independent of each other.
Based on the information provided, select Both swan and heron for the probability that a visitor to the pond will see both at least one swan and at least one heron on any given day, and select Neither swan nor heron for the probability that a visitor to the pond will see neither a swan nor a heron on any given day. Make only two selections, one in each column.
Let's solve this step by step using the independence of the two events.
Given information:- \(\mathrm{P(see\,at\,least\,one\,swan)} = 0.35\)
- \(\mathrm{P(see\,at\,least\,one\,heron)} = 0.2\)
- The events are independent
Since the events are independent, we multiply the probabilities:
\(\mathrm{P(both\,swan\,and\,heron)} = \mathrm{P(swan)} \times \mathrm{P(heron)} = 0.35 \times 0.2 = 0.07\)
First, find the probability of NOT seeing each:
- \(\mathrm{P(no\,swan)} = 1 - 0.35 = 0.65\)
- \(\mathrm{P(no\,heron)} = 1 - 0.2 = 0.8\)
Since the events are independent:
\(\mathrm{P(neither\,swan\,nor\,heron)} = \mathrm{P(no\,swan)} \times \mathrm{P(no\,heron)} = 0.65 \times 0.8 = 0.52\)
- Probability of seeing both: 0.07
- Probability of seeing neither: 0.52