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
tankabanditka [31]
3 years ago
12

Suppose you toss a coin and will win $1 if it comes up heads. If it comes up tails, you toss again. This time you will receive $

2 if it comes up heads. If it comes up tails, toss again. This time you will receive $4 if it is heads. Continue in this fashion for a total of 10 flips of the coin, after which you receive nothing if it comes up tails. What is the mathematical expectation for this game?
Mathematics
1 answer:
padilas [110]3 years ago
4 0

Answer:

5

Step-by-step explanation:

The winnings are in G.P. : 1, 2, 4, ..... till 10 toss.

$a_n = 1 \times 2^{n-1}\ \ \  \forall \ n = 1,2,3,4,....,10$

$a_n$ denotes the winnings on the $n^{th}$ toss.

The probability of earning amount $a_n$ on the $n^{th}$ toss is = $\left(\frac{1}{2}\right)^n$

∴ $E(X) = \sum_{n=1}^{10} \ a_n \times \left(\frac{1}{2}\right)^n $

            $=\sum_{n=1}^{10} \ 1 \times \frac{2^{n-1}}{2^n} $

           $=\sum_{n=1}^{10} \  \frac{1}{2}$

Sum of the 1st n terms of the A.P. is :

$=\frac{n}{2}[2a+(n-1)d] $

$=\frac{10}{2}[2\times \frac{1}{2}+(10-1)\times 0] $

= 5

Therefore, E(X) = 5

Hence the expected value of the game is 5

You might be interested in
Factor the expression completely. 1/4x + 19/4
puteri [66]

Answer: i think it is... x = -19

8 0
3 years ago
Which statement BEST explains the relationship between the numbers divisible by 6,2 and 3?
love history [14]
A. A number that is divisible by 6 is also divisible by 2 and 3 because 2 and 3 are factors of 6.
8 0
3 years ago
Read 2 more answers
A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tr
frozen [14]

Answer:

The original height of the tree is 18 m.

Step-by-step explanation:

Please see attached photo for explanation.

From the diagram, we shall determine the value of 'x'. This can be obtained by using the pythagoras theory as follow:

x² = 5² + 12²

x² = 25 + 144

x² = 169

Take the square root of both side

x = √169

x = 13 m

Finally, we shall determine the original height of the tree. This can be obtained as follow.

From the question given above, the tree was broken from a height of 5 m from the ground which form a right angle triangle with x being the Hypothenus as illustrated in the diagram.

Thus, the original height of the will be the sum of 5 and x i.e

Height = 5 + x

x = 13 m

Height = 5 + 13

Height = 18 m

Therefore, the original height of the tree is 18 m.

3 0
3 years ago
There are seven cats in my neighborhood, with an average of $41$ whiskers each. If one of the cats has $17$ whiskers, how many w
harkovskaia [24]

Answer:

Each of the other cats have 45 whiskers on average.

Step-by-step explanation:

Let x represent the average number of whisker of each cat.

We have been given that there are 7 cats in my neighborhood, with an average of 41 whiskers each.

The total number of whiskers of six cats would be 6x.

Since one of the cats has 17 whiskers, so the total number of whiskers of 7 cats would be 6x+17

We will use average formula to solve our given problem.

\text{Average}=\frac{\text{Sum of data points}}{\text{Number of data points}}

Upon substituting our given values, we will get:

41=\frac{6x+17}{7}

Let us solve for x.

41*7=\frac{6x+17}{7}*7

287=6x+17

287-17=6x+17-17

270=6x

Switch sides:

6x=270

\frac{6x}{6}=\frac{270}{6}

x=45

Therefore, the each of the other cats have 45 whiskers on average.

8 0
3 years ago
1) Find the slope and the y-byintercept of the line that passes through the points (1,5) and (3,9)
dimulka [17.4K]

Answer: slope= 2, y-intercept= 3

4 0
3 years ago
Other questions:
  • The production of health drink cans at a warehouse can be represented by the equation below, where x represents the hours of pro
    8·1 answer
  • Fill in the blanks so that the equation has the solution of x={-4,-1}
    6·1 answer
  • Find a polynomial f(x) of degree 5 that has the following zeros.
    14·2 answers
  • PLEASSSE HELP MEEE
    7·1 answer
  • A log with a radius of 2.5 feet is rolled up a hill. If it takes 30 seconds to roll the log one complete revolution, approximate
    14·1 answer
  • (Quick please ) !!!!!!!!!!!!!!!! Help me!!!!! find the surface area of the rectangular prism!!!!!! thank you
    8·1 answer
  • It is 3452 ft round trip from Craig's house to school
    14·1 answer
  • The diagonal of a TV screen is 42 inches. The base is 38
    9·2 answers
  • Pls helppp!!!!!!!!!!!!!
    12·1 answer
  • What number would represent 23 degrees below zero? *
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!