Respuesta :
Answer:
0.13
Step-by-step explanation:
We give to each rose bush in the line a number, so there are the following n possibilities that Mr Flower swill consecutively plant seven or more white bushes, firs two are that the two red bushes to be in the first three bushes planted, that is, (1 and 2) or (1 and 3) or (2 and 3). Second subset of possibilities is those red bushes to be in the last three bushes planted, that is (8 and 9) or (8 and 10) or (9 and 10), then there are a total of 6 possible options. In order to calculate the probability we need to know how many combinations of 2 bushes we can form from the total 10 bushes, it is made through the binomial coefficient.
N of possibilities is= [tex]\frac{10!}{2!(10-2)!}[/tex]=45 factorial or combination formula
Number of possible events = 6
The probability is p=[tex]\frac{6}{45}[/tex]=0.13
The probability that he will consecutively plant seven or more white bushes is 0.21 approximately.
How to calculate the probability of an event?
Suppose that there are finite elementary events in the sample space of the considered experiment, and all are equally likely.
Then, suppose we want to find the probability of an event E.
Then, its probability is given as
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text{Number of total cases}} = \dfrac{n(E)}{n(S)}[/tex]
where favorable cases are those elementary events who belong to E, and total cases are the size of the sample space.
What is chain rule in probability?
For two events A and B, by chain rule, we have:
[tex]P(A \cap B) = P(B)P(A|B) = P(A)P(B|A)[/tex]
where P(A|B) is probability of occurrence of A given that B already occurred.
If they are independent, then [tex]P(A \cap B) = P(A)P(B)[/tex]
For this case, we have:
- Total number of rose bushes to be planted = 10
- Number of white rose bushes = 8
- Number of red rose bushes = 2
P(Planting at least 7 consecutive white rose bushes) is to be found.
Total 7 consecutive white bushes are to be there, and rest of them are not of matter since they can be of any color, as we need at the least 7 of them to be white.
Probability of planting a white bush is 8/10 (total white bushes/ total bushes)
Thus, doing so 7 times consecutively, where each event of planting a bush is independent of the other, so, from the chain rule of probability and independence of these events, we get:
P(Consecutively planting 7 white bushes) = [tex]\dfrac{8}{10} \times\dfrac{8}{10} \times ... \dfrac{8}{10} \text{(7 times)} = (\dfrac{8}{10})^7 \approx 0.21[/tex]
Thus, the probability that he will consecutively plant seven or more white bushes is 0.21 approximately.
Learn more about probability here:
brainly.com/question/1210781
