Given a population comprised of 30 bats, 15 gloves, and 60 balls, if sampling is random and one at a rime without replacement,
what is the probability of obtaining a bat, a glove, and a bat in that order if three objects are sampled from the population?
Starting off, there are 105 items, of which 30 are bats. The probability for that draw is 30/105.
There are now 104 items remaining, of which 15 are gloves. The probability of getting a glove now is 15/104.
There are now 103 items remaining, of which 60 are balls. The probability of getting a ball now is 60/103.
The probability of all three occurring is the product of their individual probabilities.
60/1`06
To find the probability of obtaining a bat, a glove, and a bat in that order, we need to calculate the probability of each step and multiply them together.
Step 1: Probability of selecting a bat
There are initially 30 bats out of a total population of 30 + 15 + 60 = 105 objects. Therefore, the probability of selecting a bat as the first object is 30/105.
Step 2: Probability of selecting a glove
Once a bat has been selected, there are now 29 bats and 15 gloves remaining in the population. The total number of objects to choose from is now 29 + 15 + 60 = 104. Therefore, the probability of selecting a glove as the second object is 15/104.
Step 3: Probability of selecting a bat
Finally, after a bat and a glove have been selected, there are 28 bats and 15 gloves remaining. The total number of objects to choose from is now 28 + 15 + 60 = 103. Therefore, the probability of selecting a bat as the third object is 28/103.
To find the overall probability, we multiply the probabilities of each step together:
Probability = (30/105) * (15/104) * (28/103)
Calculating this expression will give us the final answer.
To calculate the probability of obtaining a bat, a glove, and a bat in that order, we need to find the probability of selecting each object consecutively.
Let's break it down step by step:
Step 1: Calculate the probability of selecting the first bat.
There are initially 30 bats in the population, so the probability of selecting a bat on the first draw is 30/105 (since there are 30 bats + 15 gloves + 60 balls = 105 objects in total).
Step 2: Calculate the probability of selecting a glove after selecting the bat.
After the first draw, there are now 14 gloves remaining in the population. The total number of remaining objects is now 104 (105 - 1 object already selected).
Therefore, the probability of selecting a glove on the second draw is 14/104.
Step 3: Calculate the probability of selecting another bat after selecting the glove.
After the second draw, there are now 29 bats remaining in the population. The total number of remaining objects is now 103 (104 - 1 object already selected).
Therefore, the probability of selecting a bat on the third draw is 29/103.
Step 4: Multiply the probabilities.
To find the overall probability, we multiply the probabilities from each step together:
(30/105) * (14/104) * (29/103) = 0.00352 (rounded to five decimal places).
Therefore, the probability of obtaining a bat, a glove, and a bat in that order is approximately 0.00352, or 0.352%.