can u please help me answer this question and also please write clearly so I can

Question

can u please help me answer this question and also please write clearly so I can understand thank you so much also please show all steps thank you so much

2) At a gathering of 190 college students their grade-group and major were recorded as follows: Major Grade-Group A-student B-student C-student Total Biology 20 30 20 70 Nursing Mat 10 30 10 50 Accounting Total 10 20 10 40 50 10 10 10 90 50 190 30 If a student is selected at random from this group, find the probability that the student is: Question A Biology major A Biology major or an A-student A Nursing major and a B-student. Answer Points 20IS0 -7 A Nursing major or a Biology major A math major and a Biology major An Accounting major given that they are anA-student A B-student given that they are a Math major

Explanation / Answer

Out of 190 students, 70 are from biology major so

P(biology major) = 70 /190 = 7/19 = 0.3684

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Out of 190 students, 50 are A- student so

P(A student) = 50/190

And out of 190 students 20 are biology and A student so

P(biology and A student) = 20/190

Therefore,

P(biology or A student) = P(biology) + P(A student) - P(biology and A student) = 70/190 + 50/190 - 20/190 = 100/190 = 10/19 = 0.5263

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Out of 190 students, 30 are from nursing major and B student so

P(nursing major and B student) = 30/190 = 3/19 = 0.1579

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P(nursing major) = 50/190

P(biology major) = 70/190

Since a student can be either of nursing major or biology major so

P(nursing major or biology major) = P(nursing major)+P(biology major) = (50/190) + (70/190) = 120/190 = 12/19 = 0.6316

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Since a student can be either of math major or biology major not from both so

P(math major and biology major) = 0

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Out of 50 A student , 10 are Accounting major so

P(accounting major | A student) = 10/50 = 0.200

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Out of 30 math major students, 10 are B student so

P(B-student | math major) = 10/30 = 1/3 = 0.3333

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