Loading...
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.
0.02
0.07
0.48
0.52
0.70
Let's solve this step by step using the independence of the two events.
Given information: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:
Since the events are independent:
\(\mathrm{P(neither\,swan\,nor\,heron)} = \mathrm{P(no\,swan)} \times \mathrm{P(no\,heron)} = 0.65 \times 0.8 = 0.52\)