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3 years ago

The sample space, S, for flipping a fair coin three times is shown

Mathematics

1 answer:

Ksenya-84 [330]3 years ago

3 0

Answer: $\frac{7}{8}$

Step-by-step explanation:

Given

Sample space is $={HHH,THH,HTH,HHT,TTH,THT,HTT,TTT}$

There are 8 element in sample space which indicates the outcome of tossing a coin three times

Probability of obtaining at least one head $=1-P(\text{0 head})$

$P(\text{0 head})=P(\text{All tails})$

$P=1-\frac{1}{8}$

$P=\frac{7}{8}$

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The distribution of heights of young women aged 18 to 24 is approximately normal with a mean of 64.5 inches and a standard devia

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The 68 - 95 - 99.7 rule, gives the basis to solve this question.

It says that for a normal distribution 95% of the results are between the mean minus 2 standard deviations and the mean plus 2 standard deviations.

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mean = 64.5 inches,
standard deviaton = 2.5 inches

mean - 2 standard deviations = 64.5 inches - 5 inches = 59.5 inches

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3 years ago

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3 years ago

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gi

inessss [21]

Answer:

$\frac{1429}{120}$ or $11\frac{109}{120}$

Step-by-step explanation:

Given:

A farmer has a basket of peaches. He gives ⅓ of the peaches to one person, ¼ to another, ⅕ to another, ⅛ to another, and then gives 7 peaches to a 5th person.

Remaining peaches = 4

We need to find the original number of peaches in the basket.

The farmer gives the total number of peaches = $\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7$

Let x be the former gives the total number of peaches

We multiply and divide by 120 in right side of the above equation because of 120 is divided by all given denominator and then simplify.

$x = \frac{120}{120}(\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{8}+7)$

$x = \frac{1}{120}(\frac{120}{3}+\frac{120}{4}+\frac{120}{5}+\frac{120}{8}+7\times 120)$

$x = \frac{1}{120}(40+30+24+15+840)$

$x = \frac{1}{120}(949)$

$x = \frac{949}{120}$

We add the remaining peaches by given peaches for the original number of peaches in the basket.

Original number of peaches = $\frac{949}{120}+4$

Original number of peaches = $\frac{949+4\times 120}{120}$

Original number of peaches = $\frac{949+480}{120}$

Original number of peaches = $\frac{1429}{120}$

Original number of peaches = $11\frac{109}{120}$

Therefore the original number of peaches in the basket is $\frac{1429}{120}$ or $11\frac{109}{120}$

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3 years ago