Jenna flips two pennies 105 times. How many times can she expect both coins to come up heads?

Answers

Answer 1

Answer:

The number of times that both coins come up heads will be 26.25.

What is the expected value?

In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.

The expected value is given below.

E(x) = np

Where n is the number of samples and p is the probability.

If two coins are flipped. Then the total number of the event is given as,

Total = 2 x 2 = 4 {HH, HT, TH, TT}

Favorable event = 1 {HH}

The probability of getting both same, then we have

P = 1/4

Jenna flips two pennies 105 times. Then the number of times that both coins come up heads will be given as,

E(x) = p × n

E(x) = 1/4 × 105

E(x) = 26.25

The number of times that both coins come up heads will be 26.25.

More about the expected value link is given below.

brainly.com/question/13945225

#SPJ2

Answer 2

Answer: Hi there!

Since the chance of one coin landing on heads is 1/2, we should multiply.

1/2 × 1/2 = 1/4

105 × 1/4 = 26.25

So, the answer is 26.25 times.

Hope this helps!

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In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor's degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.02 margin of error and use a confidence level of 99%. Complete parts (a) through (c) below.a. Assume that nothing is known about the percentage to be estimated.n = ________b. Assume prior studies have shown that about 55% of full-time students earn bachelor's degrees in four years or less.n = _______c. Does the added knowledge in part (b) have much of an effect on the sample size?

Answers

Answer:

(a) The sample size required is 2401.

(b) The sample size required is 2377.

Step-by-step explanation:

The confidence interval for population proportion p is:

$CI=\hat p\pm z_(\alpha/2)\sqrt{(\hatp(1-\hat p))/(n)}$

The margin of error in this interval is:

$MOE=z_(\alpha/2)\sqrt{(\hatp(1-\hat p))/(n)}$

The information provided is:

MOE = 0.02

$z_(\alpha/2)=z_(0.05/2)=z_(0.025)=1.96$

(a)

Assume that the proportion value is 0.50.

Compute the value of n as follows:

$MOE=z_(\alpha/2)\sqrt{(\hat p(1-\hat p))/(n)}\n0.02=1.96* \sqrt{(0.50(1-0.50))/(n)}\nn=(1.96^(2)*0.50(1-0.50))/(0.02^(2))\n=2401$

Thus, the sample size required is 2401.

(b)

Given that the proportion value is 0.55.

Compute the value of n as follows:

$MOE=z_(\alpha/2)\sqrt{(\hat p(1-\hat p))/(n)}\n0.02=1.96* \sqrt{(0.55(1-0.55))/(n)}\nn=(1.96^(2)*0.55(1-0.55))/(0.02^(2))\n=2376.99\n\approx2377$

Thus, the sample size required is 2377.

(c)

On increasing the proportion value the sample size decreased.

A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall. What angle will a 35-ft. ladder make the horizontal if it reaches the sample spot?

Answers

The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is $sin^(-1)(47.93)$ .

Given that,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal.

We have to find,

The angle will a 35ft.ladder make the horizontal if it reaches the sample spot.

According to the question,

A 30-ft. ladder makes an angle of 60 degrees with the horizontal when it reaches a given spot on a wall.

$sin\theta = (h)/(30) \nsin60 = (h)/(30) \n$

h = 30sin60

Then, the angle will a 35-ft. ladder make the horizontal if it reaches the sample spot.

$sin\alpha = (30sin60)/(35)\nsin\alpha = (6 sin60)/(7) \n\alpha = sin^(-1)(47.93)$

Hence, The angle will a 35-ft. ladder make the horizontal if it reaches the sample spot is $sin^(-1)(47.93)$

For more information about Trigonometry click the link given below.

brainly.com/question/19515865

So first you must find the height at which the "spot" is where the ladder touches the wall...

sin60=h/30

h=30sin60

Now we can find the angle that the 35 ft ladder make when it touches the same spot.

sinα=h/35 and using h we found earlier...

sinα=(30sin60)/35

α=arcsin[(30sin60)/35]

α≈47.93 (α≈47º55'42")

Which headline is MOST likely to be included on a national news show?“Local school raises $5,000 for cancer research”

“Iran declares war on the United States”

“School in China raises $5,000 for cancer research”

“Company closes in Alaska, lays off 2 people”

WHO EVER ANSWERS FIRST I WILL GIVE BRAINLIEST PLSE HELP ME

Answers

Answer:

I personally think B but I do not know for sure.

Step-by-step explanation:

An ordinary 52-card deck is thoroughly shuffled. You are dealt four cards. (a) What is the probability that all four cards are sevens. (b) What is the probability that at least one of the cards is a seven. (c) What is the probability that none of them are seven. (d) What is the probability that two out the four cards is a seven

Answers

Answer:

a) The probability of getting a seven is 4/52

b) At least one of the cards is a seven=0.2813

c) The probability that none of them are seven= 0.7187

d) The probability that two out the four cards is a seven= 0.043

Step-by-step explanation:

A deck contains 52 cards containing 4 sets of 13 cards . Each set has a seven card in it. Thus there are 4 seven cards in a deck of 52 cards.

a) The probability of getting a seven is 4/52=0.0769

b) At least one of the cards is a seven=

1- P(no seven)

= 1- 4C0 * 48C4/ 52C4= 1- 0.7187= 0.2813

c) The probability that none of them are seven=4C0 * 48C4/ 52C4= 0.7187

d) The probability that two out the four cards is a seven= First card is seven * second Card is seven * two cards are not seven

= 4/52* 3/51*48/50= 0.0769*0.0588*0.96= 0.043

Final answer:

The probability of drawing four sevens, at least one seven, no sevens, and exactly two sevens from a shuffled deck of cards is explained step-by-step.

Explanation:

(a) The deck contains 52 cards, out of which there are 4 sevens. So, the probability of drawing a seven on the first card is 4/52. After drawing the first seven, there are 51 cards left in the deck, including 3 sevens. So, the probability of drawing a seven on the second card is 3/51. Continuing this process, the probability of getting four sevens in a row is (4/52) * (3/51) * (2/50) * (1/49).

(b) The probability of at least one seven can be calculated by finding the probability of the complement event (no seven). The probability of no seven on the first card is 48/52. After drawing the first card, there are 51 cards left, so the probability of no seven on the second card is 47/51. Continuing this process, the probability of no seven in four cards is (48/52) * (47/51) * (46/50) * (45/49). Subtracting this probability from 1 gives us the probability of at least one seven.

(c) The probability of none of the four cards being a seven can be calculated similarly to part (b). The probability of no seven on the first card is 48/52. After drawing the first card, there are 51 cards left, so the probability of no seven on the second card is 47/51. Continuing this process, the probability of no seven in four cards is (48/52) * (47/51) * (46/50) * (45/49).

(d) To find the probability that exactly two of the four cards are sevens, we need to consider two cases: (1) the first two cards are sevens and the last two are not, and (2) the first two cards are not sevens and the last two are. The probability of the first case is (4/52) * (3/51) * (48/50) * (47/49), and the probability of the second case is (48/52) * (47/51) * (4/50) * (3/49). Adding these probabilities gives the total probability.