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3 years ago

A coin is tossed 5 times; find the probability of getting at least 1 tail. Would you consider this event likely to happen?

Mathematics

1 answer:

grin007 [14]3 years ago

6 0

Answer: 0.96875

Step-by-step explanation:

Probability of obtaining at least one tail on a toss of coin 5 times ;

P(success) in a coin toss = 1/2 = 0.5

Using the binomial distribution formula :

P(x) = nCx * p^x * (1 - p)^(n-x)

P(at least one tail) = 1 - p(0 tails)

P( 0 tails) = 5C0 * 0.5^0 * 0.5^(5-0)

= 1 * 1 * 0.03125

= 0.03125

P(at leat 1 tail) = 1 - 0.03125

P(atleast 1 tail) = 0.96875

You might be interested in

Write a compound inequality that represents the following scenario:

Inessa05 [86]

The compound inequality that represents the two following scenarios are:

65 < f ≤ 4
8 ≤ f ≤ 12

A compound inequality usually puts together two or more simple inequalities statements together.

Following the assumption from the given information that;

a free single scoop cone = f

The age group of individuals designated to receive the free single scoop cones is:

people who are older than 65 i.e. > 65
children that are 4 or under 4 i.e. ≤ 4

Thus, the compound inequality that is appropriate to express both conditions is:

65 < f ≤ 4

On Tuesdays, the least amount of flavors = 8
The addition amount of extra flavors they can add = 4

Now, we can infer that the total amount of flavors = 8 + 4 = 12

Thus, the compound inequality that is appropriate to express both conditions is:

Least amount of flavors ≤ f ≤ total amount of flavors
8 ≤ f ≤ 12

Therefore, we can conclude that the compound inequality that represents the two following scenarios are:

65 < f ≤ 4
8 ≤ f ≤ 12

Learn more about compound inequality here:

brainly.com/question/24540195?referrer=searchResults

6 0

2 years ago

An insurance company states that it settles 85% of all life insurance claims within 30 days. A consumer group asks the state ins

BlackZzzverrR [31]

Using the z-distribution, it is found that since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if there is not enough evidence that the proportion is below 85%, that is:

$H_0: p \geq 0.85$

At the alternative hypothesis, it is tested if there is enough evidence that the proportion is below 85%, that is:

$H_0: p < 0.85$

<h3>What is the test statistic?</h3>

The test statistic is given by:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

In which:

$\overline{p}$ is the sample proportion.

p is the proportion tested at the null hypothesis.

n is the sample size.

For this problem, the parameters are:

$p = 0.85, n = 250, \overline{p} = \frac{203}{250} = 0.812$

Hence the test statistic is:

$z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}$

$z = \frac{0.812 - 0.85}{\sqrt{\frac{0.85(0.15)}{250}}}$

z = -1.68

<h3>What is the p-value and the conclusion</h3>

Using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, and z = -1.68, the p-value is of 0.0465.

Since the p-value of the test is less than 0.05, we reject the null hypothesis and find that there is enough evidence to conclude that the true proportion of all life insurance claims made to this company that are settled within 30 days is less than 85%.

More can be learned about the z-distribution at brainly.com/question/16313918

#SPJ1

4 0

1 year ago

Mrs Alivia’s bathroom is in the shape of a rectangle with a width of 6 feet. Her kitchen is in the shape of a rectangle with a w

Vedmedyk [2.9K]

Answer:

1. The length of the bathroom is equal to its width. FALSE

2. Equation 2(x+6)=29 can be used to find the length of the bathroom, x.

TRUE

3. The legend of the bathroom is 11.5 feet. FALSE

4. The equation 2 x+6=29 can be used to find the length of bathroom, x.

FALSE

5. The length of the bathroom is 8.5 feet. TRUE

Step-by-step explanation:

Here, given:

The width of the bathroom = 6 feet

The width of the kitchen = 10.75 ft

The perimeter of the bathroom = 29 feet

Let us assume the length of the bathroom = k units

PERIMETER OF A RECTANGLE = 2 ( LENGTH + WIDTH)

Now, for the Mrs Avila's bathroom

29 feet = 2 (k + 6)

⇒ 29 = 2k + 12

or, 2 k = 29 - 12 = 17

⇒ k = 17/2 = 8.5 feet

So, the length of the bathroom = 8.5 units

Now, let us consider the given statements:

1. The length of the bathroom is equal to its width. FALSE

As here, Length= 8.5 units and width = 6 units

2. Equation 2(x+6)=29 can be used to find the length of the bathroom, x.

TRUE

3. The legend of the bathroom is 11.5 feet.

FALSE, the length of the bathroom is 8.5 units.

4. The equation 2 x+6=29 can be used to find the length of bathroom, x.

FALSE, the correct equation that can be used is 2x + 12 = 29

5. The length of the bathroom is 8.5 feet.

TRUE

5 0

4 years ago

Solve the in quality x plus 1<7

RUDIKE [14]

Answer:

x<6

Step-by-step explanation:

x+1 < 7

Subtract 1 from each side

x+1-1<7-1

x <6

7 0

3 years ago

I need help ! ASAP !

svetoff [14.1K]

Answer:

288

Step-by-step explanation:

There are 8 fluid ounces in a cup so that would equate to

8 x 36 = 288

288 fluid ounces a minute

7 0

3 years ago