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MAVERICK [17]
3 years ago
12

Micha is playing a game with five cards numbered 1 through 5. He will place the cards in a bag and draw one card at random three

times, replacing the card each time. To win a prize, he must draw the number 5 all three times. What is the probability he will draw the number 5 all three times?
Mathematics
1 answer:
snow_tiger [21]3 years ago
3 0

Answer: 0.008

Step-by-step explanation:

We have 3 experiments.

Each experiment is exactly the same: "Drawing the card with the number 5, out of a bag with five cards".

in a random selection all the cards have exactly the same probability of being drawn, so the probability of drawing the 5, is equal to the quotient between the number of cards with the 5 (only one) and the total number of cards in the bag (5) then the probability is:

p = 1/5.

And we want this event to happen 3 consecutive times, then the total probability is equal to the product of the probabilities for each event:

P = (1/5)*(1/5)*(1/5) = 1/125 = 0.008

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In a typical children's soccer game, there is one goal scored approximately every 18 minutes. The number of goals scored follows
Alja [10]

Answer:

2.24

Step-by-step explanation:

The probability formula using a Poisson distribution is:

P(k\ events) = \frac{\lambda^{k}e^{-\lambda}}{k!} \\\lambda\ is\ the\ average\ number\ of\ events\ per\ interval \\e\ is\ euler's\ number \\k\ is\ the\ number\ of\ events\ you\ want\ to\ calculate

λ = 90 / 18 = 5 average goals per interval (interval = a game)

So if for example you were interested in the probability of making 2 goals in a game

k = 2

P(k = 2) = \frac{5^{2}e^{-5}}{2!} = 0.084

This was just an example,

The standard deviation is \sqrt{\lambda}

\sigma = \sqrt{\lambda} \\\sigma = \sqrt{5} \\\sigma = 2.24

8 0
3 years ago
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is
aniked [119]

Answer:

10 three-point questions and 14 five-point questions.

Step-by-step explanation:

x+y = 24

3x+5y = 100

We can solve this system of equations using elimination. In order to do this, let's first multiply the first equation by 3...

3x+3y=72

3x+5y=100

Now, subtract the first equation from the second equation...

2y=28

Divide both sides by 2

y=14

Plug this back into any of the equations to solve for x...

x+14=24

x=10

There were 10 three-point questions and 14 five-point questions

7 0
2 years ago
There are 10 computers and 5 students. How many ways are there for the students to sit at the computers if no computer has more
mestny [16]

Answer:

30,240 ways

Step-by-step explanation:

This question is bothered on permutation. Permutation has to do with arrangement.

If there are 10 computers and 5 students, the number of ways students will sit at the computers if no computer has more than one student can be expressed as;

10P5 = 10!/(10-5)!

10P5 = 10!/(5)!

10P5 = 10*9*8*7*6*5!/5!

10P5 = 10*9*8*7*6

10P5 = 30,240

Hence the number of ways is 30,240 ways

6 0
3 years ago
What is the least positive integer divisible by each of the first five composite numbers
Sonbull [250]

Answer:

the answer is 360. the first composite numbers are 4,6,8,9,10

and all the numbers above are divisible by 360

360÷4=90

360÷6=60

360÷8=45

360÷9=40

360÷10=36

6 0
3 years ago
Find the mean of the data in the bar chart below.
Snowcat [4.5K]
<h2>Answer:</h2>

12

<h2>Step-by-step explanation:</h2>

<u><em>The mean is also the average.</em></u>

Add up all the number of students all together:

12+13+14+9

48

Now, Divide the total amount of students (48) by the amount of numbers you added (in this case, 48/4 because we added 4 numbers wich are 12+13+14+9)

The average amount of students is 12

7 0
2 years ago
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