The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the intersection of being a junior and participating in marching band?

0.89
0.39
0.16
0.73

Question

madisonmichellew madisonmichellew

18-05-2021
Mathematics

contestada

The students who attend Memorial High School have a wide variety of extra-curricular activities to choose from in the after-school program. Students are 38% likely to join the dance team; 18% likely to participate in the school play; 42% likely to join the yearbook club; and 64% likely to join the marching band. Many students choose to participate in multiple activities. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the intersection of being a junior and participating in marching band?

0.89
0.39
0.16
0.73

Respuesta :

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elyseclark11 elyseclark11 · Answer 1 · 2021-05-28T19:08:45+02:00

elyseclark11 elyseclark11

28-05-2021

Answer:

0.16

Step-by-step explanation:

I took the test

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anuksha0456 anuksha0456 · Answer 2 · 2022-05-29T14:46:37+02:00

Probability of the intersection of being a junior and participating in marching band = 0.16

What do we mean by Probability?

The probability of an event taking place is the numeric value determining how likely that particular event is to take place.

It is determined by the formula,

Probability( Event ) = Number of favorable outcomes for that event/Total number of outcomes.

The summation of all probabilities for a given event is 1.

What do we mean by the intersection of Probabilities?

The intersection of Probabilities is just the product of the two probabilities.

How do we solve the given question?

In the question, we are said that students have equal probabilities of being freshmen, sophomores, juniors, or seniors.

∴ Probability(A student is a junior) = 1/4 = 0.25, as we have 4 cases all equally probable.

Now, we are said that a student is 64% likely to join the marching band.

∴ Probability( A student joins marching band) = 64% = 64/100 = 0.64.

We are asked to find the probability of the intersection that a student is a junior and participates in the marching band.

Probability( A student is a junior and joins marching band) = Probability( A student joins marching band)* Probability( A student is a junior)

∴ Probability( A student is a junior and joins marching band) = 0.64*0.25 = 0.16

∴ Probability of the intersection of being a junior and participating in marching band = 0.16

Learn more about Probability at

https://brainly.com/question/24756209

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