Question

Mr. Flowers plants 10 rose bushes in a row. Eight of the bushes are white and two are red, and he plants them in random order. What is the probability that he will consecutively plant seven or more white bushes?

Answer 1

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=  $\frac{10!}{2!(10-2)!}$=45 factorial or combination formula

Number of possible events = 6

The probability is p=$\frac{6}{45}$=0.13