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deff fn [24]
3 years ago
12

If you roll 5 dice what is the probability of getting exactly 3 dices with 4 and two something other than 4

Mathematics
1 answer:
ollegr [7]3 years ago
4 0

When you roll a die, you get 4 with probabiliy 1/6 and something other than 4 with probability 5/6.

You want to get 4 three times, this happens with probability (1/6)^3.

You want to get something other than 4 two times, this happens with probability (5/6)^2.

Finally, we have to count all the combinations of three rolls ending in 4 and two rolls ending in something other than 4. For example, you might have

44NN4

4N4N4

N44N4

(where '4' represents a roll ending in 4 and 'N' represents a roll ending in something other than 4)

The number of different combinations is given by the binominal coefficient (5 3), because choosing the roll that must end in 4 automatically fixes also those that won't end in 4:

\displaystyle \binom{5}{3}=\dfrac{5!}{3!2!}=\dfrac{5\times 4\times 3\times 2}{3\times 2\times 2}=10

So, the final anwer is

10\left(\dfrac{1}{6}\right)^3\cdot\left(\dfrac{5}{6}\right)^2

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A game is being played with two players. There are 21 balloons and the player who pops the last balloon wins. One or two can be
34kurt

Answer:

  be the second player, and always leave a multiple of 3 balloons

Step-by-step explanation:

In order to win, a player must force the other player to leave one or two balloons. To do that, the winning player must leave one more balloon than the maximum number that can be popped. That is, the winner will be the player who leaves 3 balloons,

Working backward, we find that the winner must leave a multiple of 3 after each turn. Since the starting number is a multiple of 3, the first player must lose if the second player plays optimally.

The winning strategy is ...

  • be the second player
  • always leave a multiple of 3 balloons.
4 0
3 years ago
Solve this system of linear equations. separate x and y values with a comma. 7x=-67-11y 5x=-73-11y​
Aleks [24]

Answer:

3, -8

(x is equal to 3 and y is equal to -8)

Step-by-step explanation:

<u>The system:</u>

{ 7x=-67-11y

{ 5x=-73-11y​

<u>Finding a value for x:</u>

7x=-67-11y -> x = -\frac{67}{7} - \frac{11y}{7}

<u>Solving for y by plugging in our x:</u>

[Equation] 5x = -73 -11y​

[Plug-in] 5(-\frac{67}{7} - \frac{11y}{7}) = -73 -11y​

[Distribute the 5] -\frac{335}{7} - \frac{55y}{7} = -73 -11y​

[Multiply by 7] 7 (-\frac{335}{7} - \frac{55y}{7}) = (-73 -11y​) 7

[Simplify] -335 - 55y = -511 - 77y

[Add 335 and 77y to both sides] 22y = -176

[Divide by 22] y = -8

<u>Plug in our y to solve for x:</u>

5x = -73 -11y​

5x = -73 -11(-8)

5x = -73 + 88

5x = 15

x = 3

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

5 0
3 years ago
Solve for a in terms of F and m: F=ma
Elena-2011 [213]
To solve for a, you must get a by itself on one side of the equation.  Now, a is "joined" to m by multiplication.  To "separate" them, use the inverse operation, division.

Divide both sides of the equation by m.

F=ma \\ \frac{F}{m}=\frac{ma}{m} \\ \frac{F}{m}=a \\ a=\frac{F}{m}
5 0
3 years ago
Which of the following is an arithmetic sequence?
Mashcka [7]
The following answer would be D because I’m guessing and I need the answers too sorry
6 0
3 years ago
The ratio of male to female students in a junior high
nalin [4]

the total no of population=1650

13:17 first add the two numbers 13+17=30

then 13/30×y =715 , i make 13 at the numerator because it's males ratio

after that 30/13×13/30y =715 ×30/13

y =715×30/13

y =1650

after u find the total no it's simple to find the no of females

17/30×1650=935

8 0
3 years ago
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