10. A school is trying to schedule periods of Chemistry and Algebra II.
They find that a total of 386 students are taking either one or both of
the two courses. If 298 students signed up for Algebra II and 328 have
signed up for Chemistry, what would be the probability that a student
chosen at random from the 386 will be signed up for both of the
courses? Round your answer to the nearest whole number percent.

Question

06-06-2020
Mathematics

contestada

10. A school is trying to schedule periods of Chemistry and Algebra II.
They find that a total of 386 students are taking either one or both of
the two courses. If 298 students signed up for Algebra II and 328 have
signed up for Chemistry, what would be the probability that a student
chosen at random from the 386 will be signed up for both of the
courses? Round your answer to the nearest whole number percent.

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isyllus isyllus · Answer 1 · 2020-06-11T04:03:09+02:00

Answer:

~62%

Step-by-step explanation:

Let n(A) be the number of students signed up for Algebra II.

Given that n(A) = 298

Let n(B) be the number of students signed up for Chemistry.

Given that n(B) = 328

n(A [tex]\cup[/tex] B) will be the number of students who have signed up for either one or both of two subjects.

n(A [tex]\cup[/tex] B) = 386

Formula for n(A [tex]\cup[/tex] B):

n(A [tex]\cup[/tex] B) = n(A) + n(B) - n(A [tex]\cap[/tex] B)

Where n(A [tex]\cap[/tex] B) is the number of students signed up for both the courses.

Putting the values in the formula above:

386 = 298 + 328 - n(A [tex]\cap[/tex] B)

n(A [tex]\cap[/tex] B) = 240

Formula for Probability of an event E:

[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]

[tex]P(A \cap B) = \dfrac{n(A \cup B) }{n(A \cap B)}[/tex]

[tex]\Rightarrow P(A \cap B) = \dfrac{240 }{386}\\\Rightarrow P(A \cap B) = 62.17\%[/tex]

Hence, the required probability is ~62%

andromache andromache · Answer 2 · 2022-03-17T14:36:27+01:00

The probability that a student chosen at random from the 386 will be signed up for both of the courses should be 62%.

Calculation of the probability:

Since total of 386 students are taking either one or both of the two courses. If 298 students signed up for Algebra II and 328 have signed up for Chemistry

So here the no of students that signed up for both subjects should be

= 298 + 328 - 386

= 240

Now the probability is

[tex]= 240\div 386[/tex]

= 62%

Hence, The probability that a student chosen at random from the 386 will be signed up for both of the courses should be 62%.

Learn more about probability here: https://brainly.com/question/16923992