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
Serhud [2]
3 years ago
12

"What is the probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice? Assume you’re throwing a single d

ie each time."
Mathematics
1 answer:
dem82 [27]3 years ago
5 0

Answer:

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

Step-by-step explanation:

For each throw, there are only two possible outcomes. Either it is a '3', or it is not. This means that we solve this problem using the binomial probability distribution.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinatios of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

In this problem we have that:

There are 6 possible outcomes for the dice. This means that the probability that it is a '3' is \frac{1}{6} = 0.167

There are 10 throws, so n = 10.

Probability of throwing AT LEAST two ‘3’s on the dice?

Either you throw less than two, or you throw at least two. The sum of the probabilities of these events is 1. So

P(X < 2) + P(X \geq 2) = 1

P(X \geq 2) = 1 - P(X < 2).

In which

P(X < 2) = P(X = 0) + P(X = 1).

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 0) = C_{10,0}.(0.167)^{0}.(0.833)^{10} = 0.1609

P(X = 1) = C_{10,1}.(0.167)^{1}.(0.833)^{9} = 0.3225

So

P(X < 2) = P(X = 0) + P(X = 1) = 0.1609 + 0.3225 = 0.4834.

Finally:

P(X \geq 2) = 1 - P(X < 2) = 1 - 0.4839 = 0.5161.

There is a 51.61% probability that in 10 dice throws, you will throw AT LEAST two ‘3’s on the dice.

You might be interested in
Anyone know how to do this with a explanation ?
storchak [24]

Answer:

30 degrees

Step-by-step explanation:

Since we know that all triangles equal 180 degrees, we can add the 2 given angles and subtract that from 180 to find the remaining angle.

90+60=150

180-150=30 degrees

8 0
3 years ago
Divide 45 sweets between two girls in to the given ratio of 4:5​
Eva8 [605]

Answer:

Therefore, the two equivalent ratios of 4 : 5 are 8 : 10 and 12 : 15.

Step-by-step explanation:

7 0
2 years ago
What is 188.8 rounded to the nearest hundredth
My name is Ann [436]

Answer:

188.80 to the nearest hundredth

7 0
3 years ago
Demand for your tie-dyed T-shirts is given by the formula q = 510 − 90p0.5 where q is the number of T-shirts you can sell each m
telo118 [61]

Answer:

The demand will drop approximately 23 T-shirt per month.

Step-by-step explanation:

Consider the provided formula.

q = 510-90p^{0.5}

You currently sell T-shirts for $15 each and you raise your price by $2 per month,

That means p=$15 and \frac{dp}{dt}=2

We need to find how fast demand will drop.

So differentiate the above function with respect to time.

\frac{dq}{dt} =0-45p^{0.5-1}\frac{dp}{dt}

\frac{dq}{dt} =-45p^{-0.5}\frac{dp}{dt}

Substitute the respective values as shown:

\frac{dq}{dt} =-45(15)^{-0.5}(2)

\frac{dq}{dt} \approx-23.24

Hence, the demand will drop approximately 23 T-shirt per month.

3 0
3 years ago
Heeelllllppp ASAAPPPPP
Nutka1998 [239]
The answer is 351.8.
4 0
3 years ago
Read 2 more answers
Other questions:
  • Which equation represents a graph with a vertex at (1, –6)?
    12·2 answers
  • Plz someone help me, this is due in 45mins
    14·2 answers
  • 45 points! Help me on the attached file, please :D
    6·1 answer
  • What is the domain and range of the set of ordered pairs?​
    5·1 answer
  • Find the height of a cylinder with radius 25 cm and surface area 8953.54 cm2.
    9·1 answer
  • Solving quadratic equation using the completing the square (a).<br>9k²+5k=2​
    14·1 answer
  • 2. ART An artist created a statue in the shape of a
    10·1 answer
  • Pls help I need a good grade
    13·1 answer
  • Help help help please please please
    6·1 answer
  • What is the value of x?
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!