1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
maw [93]
1 year ago
8

A frog moves in a sequence of unit steps. Each step is N, S, E or W with equal probability. It starts at the origin. Find the pr

obability that it reaches (2, 2) in less than 7 steps.
Mathematics
1 answer:
Molodets [167]1 year ago
4 0

The answer is 067.

It takes an even number of steps for the object to reach (2,2), so the number of steps the object may have taken is either 4 or 6 .

If the object took 4 steps, then it must have gone two steps $\mathrm{N}$ and two steps E, in some permutation. There are $\frac{4 !}{2 ! 2 !}=6$ ways for these four steps of occuring, and the probability is $\frac{6}{4^{4}}$.

If the object took 6 steps, then it must have gone two steps N and two steps E, and an additional pair of moves that would cancel out, either N / S or W/E. The sequences N, N, N, E, E, S can be permuted in $\frac{6 !}{3 ! 2 ! 1 !}=60$ ways. However, if the first four steps of the sequence are N, N, E, E in some permutation, it would have already reached the point (2,2) in four moves. There are $\frac{4 !}{2 ! 2 !}$ ways to order those four steps and $2 !$ ways to determine the order of the remaining two steps, for a total of 12 sequences that we have to exclude. This gives $60-12=48$ sequences of steps. There are the same number of sequences for the steps N, N, E, E, E, W, so the probability here is $\frac{2 \times 48}{4^{6}}$.

The total probability is $\frac{6}{4^{4}}+\frac{96}{4^{6}}=\frac{3}{64}$, and $m+n=067$.

What is probability?

  • Probability is synonymous with possibility. It is a mathematical discipline that deals with the occurrence of a random event. The value ranges from zero to one.
  • Probability has been introduced in mathematics to predict the likelihood of occurrences occurring. Probability is defined as the degree to which something is likely to occur.
  • This is the fundamental probability theory, which is also utilized in probability distribution, in which you will learn about the possible results of a random experiment.
  • To determine the likelihood of a particular event occurring, we must first determine the total number of alternative possibilities.

To learn more about probability visit:

brainly.com/question/11234923

#SPJ4

You might be interested in
What two consecutive whole numbers lie between the square root of 55?
Kamila [148]
\boxed{7 \ \textless \  \sqrt{55} \ \textless \  8}\\\\because\ 7^2=49 \ \textless \  55\ and\ 8^2=64 \ \textgreater \  55
6 0
3 years ago
Read 2 more answers
Does anyone know the answer to this¿?¿
natita [175]
The answe is y=25 and theres 5$
7 0
3 years ago
Math graph equation. <br> (Picture.)
vladimir1956 [14]

Answer:

y = -2x + 3 is the required equation

Step-by-step explanation:

From the graph we will get two ordered pairs

If we see that When x=0 then y=3  and when x = 1 then  y=1

Now from this we can find the slope of the Graph

So slope of graph = (y2 - y1) / (x2-x1)

                               =(1-3) / (1-0)

                                =-2

So

Slope = m = -2

Now the equation is

y = mx + b

We have to find the value of b

as we have two ordered pairs we can take any of it to find the value of b because line passes through those points

taking (0,3) as a point

y= mx + b

put values

3 = -2*(0) + b

so

b=3


Now the equation of the line in this form is

y = mx + b

which is

y = -2x + 3

5 0
3 years ago
On a map, a clothing store ia located at (-2,-3). A seafood restaurant is located 6 units to the right of the clothing store. Wh
Serhud [2]
The coordinates would be (4,-3)
6 0
3 years ago
Read 2 more answers
I need help. Find the value of each variable.
azamat

Answer:

x=8, y=4\sqrt{3}

Look up the 30-60-90 triangle rule

8 0
2 years ago
Read 2 more answers
Other questions:
  • Natalie is shopping at a used book and music store. A sign advertise 4 cds for $12. What is the unit rate for the cost of 1 cd?
    9·2 answers
  • If 75 is 25% of a value, what is that value? A. 300 B. 100 C. 350 D. 225
    13·1 answer
  • Why does it take 3 copies of 1/6 to show the same amount as 1 copy of 1/2
    6·2 answers
  • Carrie planted 48 tulips in 12 minutes how many tulips did she plant per minute
    13·2 answers
  • Three times the lesser of the two consecutive even integers is six less than six times the greater number find the integers how
    9·1 answer
  • Any Help would be appreciated!!<br><br> Multiply.<br><br> (5 − 1)(6^2 + 3 + 7)
    8·2 answers
  • Translate the following words into an algebraic expression.
    15·2 answers
  • 3/10 + 4/100 = write as a fraction.
    11·2 answers
  • Hurrrrrrrryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy
    7·2 answers
  • Write 0.15 as a fraction in simplest form. 0.15 =​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!