A study of birds in California found 120 hummingbirds, 40 robins, 30 warblers, and 10 mockingbirds.
a) If a bird is randomly chosen from this study, what is the probability that it will be a hummingbird?
b) If a bird is randomly chosen from this study, what is the probability that it will be a robin or mockingbird?
c) If two birds are randomly chosen from this study, what is the probability that one will be a robin and the other will be mockingbird?
I tired these problems on my own and the answers I got were: a) 0.60 b) 0.25 and c) 0.25 but I am not sure if these are right.
(a) and (b) are ok, but
(c) is
2 * 40/200 * 10/199
that is P(robin,mocker) + P(mocker,robin)
(d) If an bird is randomly chosen from the population and then returned to the population (total number of birds is the same for all trials), what is the probability that we will select a hummingbird, then a mockingbird, and then a warbler?
how would I go about doing this?
since each draw is taken from the total population of 200 birds, that would be
120/200 * 10/200 * 30/200
To find the probabilities, you need to consider the total number of birds and the number of each type of bird in the study. Let's go through each question step by step:
a) Probability of choosing a hummingbird:
To find the probability of choosing a hummingbird, divide the number of hummingbirds by the total number of birds in the study.
Number of hummingbirds = 120
Total number of birds = 120 + 40 + 30 + 10 = 200
Probability (hummingbird) = Number of hummingbirds / Total number of birds = 120 / 200 = 0.6
So you are correct. The probability of randomly choosing a hummingbird is 0.6.
b) Probability of choosing a robin or mockingbird:
To find the probability of choosing a robin or mockingbird, add the number of robins and mockingbirds together, and then divide by the total number of birds in the study.
Number of robins = 40
Number of mockingbirds = 10
Probability (robin or mockingbird) = (Number of robins + Number of mockingbirds) / Total number of birds = (40 + 10) / 200 = 50 / 200 = 0.25
Your answer for this question is also correct. The probability of randomly choosing a robin or mockingbird is 0.25.
c) Probability of choosing one robin and one mockingbird:
To find the probability of choosing one robin and one mockingbird, you need to consider the number of possible ways you can choose one robin and one mockingbird divided by the total number of possible pairs of birds.
Number of robins = 40
Number of mockingbirds = 10
Number of possible ways to choose one robin and one mockingbird = Number of robins * Number of mockingbirds = 40 * 10 = 400
Total number of possible pairs of birds = Total number of birds choose 2 = (Number of birds)*(Number of birds - 1) / 2 = (200)*(199) / 2 = 19900
Probability (one robin and one mockingbird) = Number of possible ways to choose one robin and one mockingbird / Total number of possible pairs of birds = 400 / 19900 = 0.0201
Your answer for this question is incorrect. The correct probability of randomly choosing one robin and one mockingbird is approximately 0.0201.