A builder has 8 lots available for sale.
· Six lots are greater than one acre.
· Two lots are less than one acre.
What is the probability that the next three lots sold will be greater than one acre?
call them b , for "big" and s for "small"
so you have 6 b's and 2 s's
prob = (6/8)(5/7)(4/6) = 120/336 = 5/14
To find the probability that the next three lots sold will be greater than one acre, we need to calculate the probability of selecting a lot greater than one acre for each of the three sales, assuming no replacement.
First, let's calculate the probability of selecting a lot greater than one acre for the first sale. There are 6 lots greater than one acre out of 8 total lots, so the probability is 6/8 = 3/4.
Since we assume no replacement, after the first sale, there will be 5 lots greater than one acre left out of the remaining 7 lots.
For the second sale, the probability of selecting a lot greater than one acre is 5/7.
Similarly, after the second sale, there will be 4 lots greater than one acre left out of the remaining 6 lots.
For the third sale, the probability of selecting a lot greater than one acre is 4/6.
To find the overall probability, we multiply the probabilities of each sale together:
(3/4) * (5/7) * (4/6) = 15/56
Therefore, the probability that the next three lots sold will be greater than one acre is 15/56.
To find the probability that the next three lots sold will be greater than one acre, we need to know the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of outcomes. We know that the builder has 8 lots available for sale, so there are 8 possible outcomes.
Next, let's determine the number of favorable outcomes. We are looking for the next three lots sold to be greater than one acre. We are given that six lots are greater than one acre initially, and we need to find the probability for three more lots being greater than one acre. Since each lot is chosen independently, the probability of each lot being greater than one acre remains the same. Therefore, the probability for each lot being greater than one acre is 6/8.
To find the probability of multiple independent events occurring, we multiply their probabilities together. In this case, we need all three lots to be greater than one acre, so we multiply 6/8 by itself three times:
(6/8) * (6/8) * (6/8) = 216/512 = 27/64
So, the probability that the next three lots sold will be greater than one acre is 27/64.