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
Hamburger: $6.00<br> Fries: $2.00<br> Tax: 7%<br> Tip: 20%<br><br> Total: ___
Salsk061 [2.6K]

Answer:

$10.27

Step-by-step explanation:

H + F = $8, (7% of 8 is 0.56) [$8.56] + 20% = 10.272 --> $10.27

3 0
3 years ago
500 grams of tomatoes cost £1.76 how much will 1.75kg cost??
ValentinkaMS [17]
500 grams equals 0.50 kg so multiply 1.76 3 times to get 5.28, then divide 1.76 by 2 to get .88 add the two together to get 6.16
3 0
3 years ago
Solve for the width in the formula for the area of a triangle
zmey [24]

Answer: \frac{2A}{h} = w

Step-by-step explanation:

The formula for area of a triangle is A = wh\frac{1}{2}

Now we have to isolate for w.

First multiply by the 2 which is the reciprocal of 1/2 to cancel it out.

2A = wh\\

Now divide by h to isolate w.

\frac{2A}{h} = w

4 0
2 years ago
yo i need help with this question please and thank u i need the correct answer to please i will give u a brainliest as well
Simora [160]
V = πr ^2 h
V = π (3)^2 (5)
V = π (9) (5)
V = π 45
V = 141.3 in
141.3 divided by 8 = 17.7
8 0
2 years ago
What is the value of |−44|?
yan [13]
Absolute value is simply the distance from zero on a number line. -44 is 44 away from zero, so the absolute value of -44 is

44
8 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the inequality -24&lt;×-3-8×. A.×&gt;-3 B. ×&lt;3 C.×&gt;-9 D.×&gt;3
    7·1 answer
  • the big dog weighs 5 times as much as the little dog. The little dog weighs 25% as much as the medium sized dog. The medium size
    10·1 answer
  • Question 3: Solve the Variables<br> Will give brainliest, must show work and answers!
    5·1 answer
  • A laundry detergent box measures 12 inches by 8 inches by 2.5 inches. What is the volume of two boxes of detergent ?
    10·1 answer
  • Michelle collected 7 more than twice the number of newspaper David collected. Michelle collected 33 newspaper. How many did Davi
    11·1 answer
  • What is the minimum value of the parabola y= x^2+5x
    6·1 answer
  • Suppose that 30% of a population carries a certain gene. You want to estimate the probability that it will take at least a sampl
    10·1 answer
  • You have this information about ΔABC, ΔFDE, and ΔGIH:
    8·2 answers
  • If a shuttle can go 28,000km per hour, how long will it take for the shuttle to go 1,277,127,530 km?
    10·2 answers
  • Please help me I really don’t know
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!