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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

You might be interested in
Eric's class consists of 12 males and 16 females. If 3 students are selected at random, find the probability that they
Reptile [31]

Answer:

The probability that all are male of choosing '3' students

P(E) = 0.067 = 6.71%

Step-by-step explanation:

Let 'M' be the event of selecting males n(M) = 12

Number of ways of choosing 3 students From all males and females

n(M) = 28C_{3} = \frac{28!}{(28-3)!3!} =\frac{28 X 27 X 26}{3 X 2 X 1 } = 3,276

Number of ways of choosing 3 students From all males

n(M) = 12C_{3} = \frac{12!}{(12-3)!3!} =\frac{12 X 11 X 10}{3 X 2 X 1 } =220

The probability that all are male of choosing '3' students

P(E) = \frac{n(M)}{n(S)} = \frac{12 C_{3} }{28 C_{3} }

P(E) =  \frac{12 C_{3} }{28 C_{3} } = \frac{220}{3276}

P(E) = 0.067 = 6.71%

<u><em>Final answer</em></u>:-

The probability that all are male of choosing '3' students

P(E) = 0.067 = 6.71%

3 0
3 years ago
4. A boat sails east for 35 miles and then turns to sail 10 miles south. What is the distance of the boat from its ending point
Elden [556K]

Answer:

36.4mi

Step-by-step explanation:

The boat sailed two legs of a right-angled triangle.

The distance from the starting point is the hypotenuse of the triangle.

d = √(35² + 10²)

  = √(1225 + 100)

  = √1325

  = 36.4 mi

5 0
3 years ago
D. (1/2)n +7 = (n+14)/2
TEA [102]

Answer:

n=-14

Step-by-step explanation:

4 0
3 years ago
How to solve 3(4y+2)
weeeeeb [17]

Answer:

12y+6

Step-by-step explanation:

You have to use the distributive property and do 3 x 4y and 3 x 2 and you get 12y+6.

3 0
2 years ago
F(x)=2x^3+2x-3 g(x)=-.5[x-4] what is the y value when f(x) = g(x)?
Charra [1.4K]

Answer:

D. x = 0.5

Step-by-step explanation:

A graphing calculator is the quickest way to get to an answer here.

 f(x) = g(x) for x = 0.5

__

We can find the y-intercepts of the two functions to be ...

 f(0) = -3

 g(0) = -2

We know the x-intercept of g(x) is x=4. The x-intercept of f(x) will be a value less than 1, because f(1) = 1. (The function crosses the x-axis between x=0 where f(x) < 0 and x=1, where f(x) > 0.)

Considering these intercept points, we know the value of x for f(x)=g(x) will be between x=0 and x=1. There is only one answer choice in that interval:

 x = 0.5

5 0
3 years ago
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