Mathematics, 22.06.2019 18:10 Harambe659

An instructor gives her class a set of 10 problems with the information that the final exam will consist of a random selection of 5 of them. if a student has figured out how to do 7 of the 10 problems, what is the probability that he will answer correctly (a) all 5 problems? (b) at least 4 of the problems?

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Answer from: angelrgomez01

Answer with explanation:

It is given that An instructor gives her class a set of 10 problems.

The final exam will consist of a random selection of 5 of them.

A student has figured out how to do 7 of the 10 problems.

We know that the probability of an event is defined as the ratio of number of favorable outcomes to the total number of outcomes.

The probability that he will answer all the 5 problems correctly is:

given by:

$\dfrac{7_C_5}{{10}_C_5}$

Since he may chose 5 questions out of 7 questions that a student knows how to do and total outcomes is the selection of 5 questions from the total 10 questions.

Hence, on solving we get:

$=\dfrac{\dfrac{7!}{5!\times (7-5)!}}{\dfrac{10!}{5!\times (10-5)!}}\\\\\\\\=\dfrac{\dfrac{7!}{5!\times 2!}}{\dfrac{10!}{5!\times 5!}}$

On further solving we get:

Probability=0.083

The probability that he will answer at least four correctly is given by:

$\dfrac{7_C_4\times 3_C_1+7_C_5}{10_C_5}$

( Since, he may answer correctly four or five questions)

( If he answer four answers correctly, this means he choose 4 questions from 7 questions and 1 from the remaining.

and if he answers five answer correctly then he choose it from the 7 questions a student know)

Hence, on solving we get:

$Probability=\dfrac{2}{9}\\\\\\Probability=0.222$

Hence, we get Probability= 0.222

Answer from: Quest

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

Answer from: Quest

Ithink the answer will be 5

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