I need help with a math problem

If you flip a fair coin 4 times, what is the probability that you will get exactly 2 tails

Answer:

<h3>The answer is <u>3/8</u> NOT 50%</h3>

Step-by-step explanation:

One way to solve this problem is to figure out how many ways you can get exactly 222 tails, then divide this by the total number of outcomes you could have gotten. Since every outcome has equal probability, this will be the probability that you will get exactly 2 tails.

How many outcomes are there where you get exactly 2 tails? Try thinking of each outcome as a 4-letter word, where the first letter is "H" if the first coin toss was heads and "T" if it was tails, and so on.

So, the number of outcomes with exactly 2 tails is the same as the number of these words which have 2 T's and 2 H's.

How many of these are there? If we treat all the letters as unique, we'll find that there are 4! different arrangements, overcounting 2! times for every time we only switch the T's around, and 2! times for every time we only switch the H's around.

So, there are <u>4!/2!2!</u> = 6

<u>4!/2!2!</u>= 6 different outcomes where you get exactly 2 tails.

Altogether, there are 2^4 = 16 total possible outcomes.

So, the probability that you will get exactly 2 tails is <u>6/16</u> = 3/8

4 0

3 years ago

In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will

love history [14]

Answer:

1. JG (Jim gets first prize, George gets second prize)

2. JH (Jim gets first prize, Helen gets second prize)

3. JM (Jim gets first prize, Maggie gets second prize)

4. GH (George gets first prize, Helen gets second prize)

5. GJ (George gets first prize, Jim gets second prize)

6. GM (George gets first prize, Maggie gets second prize)

7. MJ (Maggie gets first prize, Jim gets second prize)

8. MG (Maggie gets first prize, George gets second prize)

9. MH (Maggie gets first prize, Helen gets second prize)

Step-by-step explanation:

The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.

The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.

4 0

2 years ago

Slope of line -3,7 3,15

MissTica

Answer:

Step-by-step explanation:

8 0

3 years ago

I need help <br> 22 points to whoever helps me

Olenka [21]

Answer:

12 3/4 same slope fro both

13 DE = 5, CB = 10

14 see below

Step-by-step explanation:

12. the slopes are the same

D(0, 3) E(4, 6) slope is (change in y)/(change in x)

change in y = 3 to 6 is a change of +3

Change in x = 0 to 4 is a change of +4

slope is 3/4

13 To fine lengths you can distance formula or Pythagorean theorem (spoiler: they are related to each other)

DE² = 3² + 4²

DE² = 9 + 12

DE² = 25

√DE² = √25 = 5

DE = 5

and

CB² = 6² + 8²

CB² = 36 + 64

CB² = 100

√CB² = √100 = 10

CB = 10

14. since the slopes are the same are DE is 1/2 or CB its is the mid segment. because (taken from mathopenref.com/trianglemidsegment.html)

The midsegment is always parallel to the third side of the triangle. In the figure above, drag any point around and convince yourself that this is always true.

The midsegment is always half the length of the third side. In the figure above, drag point A around. Notice the midsegment length never changes because the side BC never changes.

A triangle has three possible midsegments, depending on which pair of sides is initially joined.

6 0

2 years ago

Please help

Schach [20]

Answer:

Hence, option: B is correct (11.02 seconds)

Step-by-step explanation:

Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.

Now we are asked:

How long does it take for the ball to reach the ground?

i.e. we have to find the value of t such that height is zero i.e. h(t)=0.

$-0.075t2+0.6t+2.5=0$

or $0.075t^2-0.6t-2.5=0$

i.e. we need to find the roots of the above quadratic equation.

on solving the equation we get two roots as:

t≈ -3.02377 and t≈11.0238

As time can't be negative; hence we will consider the value of t as t≈11.0238.

Hence it takes 11.02 seconds for the ball to reach the ground.

Hence option B is correct (11.02 seconds).

7 0

3 years ago

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