A small high school surveyed 52 of its seniors about their plans after they grad

Question

A small high school surveyed 52 of its seniors about their plans after they graduate. They found the following data and wanted to analyze it based on gender. In this case, If we pick a student at random we can place them into one of four events. M = Male F = Female C - Going to College N = Not going to College a) What is the probability that a person picked at random would be female P(F)? b) What is the probability that a person picked at random would be going to college P(c)? c) What is the probability that a person picked at random would be female and going to college p(F and C)? d) Are the event F and c mutually exclusive Explain. e) Find the probability of Female or Going to College P(F or C). f) Are the events Male or Female mutually exclusive? Explain. g) Find the probability of Male or Female P(M or F). h) Find the probability that a person chosen from the high school goes to college given that the person is female P(C|F). i) Find the probability that a person chosen from the high school is female given that the person if going college P(F|C).

Explanation / Answer

first we create table for given problem

52

a)

person picked at random will be female p(F)

p(event occure)= chances that event will be occure / Total event

so out of 52 there are 22 women ,

so p(F)=22/52=0.423

b)

person picked at random would be going to college i.e p(C)

p(Event Occure)= chances that event will be occure / Total event

so out of 52 there are 29 peson are going to college

so p(F)=29/52=0.558

   c)

person picked at random would be female and going to college i.e p(F and C)=P(F C)

p(Event Occure)= chances that event will be occure / Total event

so out of 52 there are13 Female who are going to college

so ,P(F C)=13/52=0.25

   d)

are the event F and C are mutually exclusive.

Event E1 and E2 are said to be mutually exclusive if E1 and E2 will not happen together. So the probabality of the 2 events will be zero: i.e.

P(E1 and E2) = 0.

but in our case P(E1 and E2) = P(F and C)= 13/52 =0.25 which is not equal to zero

so the event F and C are not mutually exclusive.

E)

person picked at random would be female OR going to college i.e p(F or C)=P(F   C)

p(Event Occure)= chances that event will be occure / Total event

out of 52 there are 22 Female and we also have to add 16 male who are going to college ,

so ,P(F C)=38/52=0.730

F).

Event E1 and E2 are said to be mutually exclusive if E1 and E2 will not happen together. So the probabality of the 2 events will be zero: i.e.

P(E1 and E2) = 0.

but in our case P(E1 and E2) = P(M and F)= 0

so the event M and F are mutually exclusive.

G)

p(M or F)= P(M F)

Prob that selecte d person is male or female= (30+22)/52=1

H)

we have given that selected person is female ,so there are only 22 female ,they ask us to calculate weather selected person is going to college .

so out of 22 there are 13 female who are ging to college

p(C given F)=13/22=0.590

i)

we have given that selected person isgoing to college ,so there are only 29 person who are going to college,they ask us to calculate weather selected person is female .

so out of 29 there are 13 female who are ging to college

p(C given F)=13/29=0.448

Male M Female F Total Going to College C 16 13 29 Not going to college N 14 9 23 Total 30 22

52

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