Respuesta :
Answer:
(a) The probability of the event that a student owns a stock is 0.35.
The probability of the event that a student owns a mutual fund.
(b)The probability that a student owns neither a stocks nor mutual is 0.5.
(c)The probability that a student owns either a stocks or a mutual fund is 0.80.
Step-by-step explanation:
Probability:
Let the event space S of a given random experiment E be finite. If all the simple events connected to E be 'equally likely' then the probability of event A is defined as
[tex]P(A)=\frac mn[/tex]
where n is total number of sample event and of these simple events are favorable.
Formula:
P(A∪B)=P(A)+P(B)-P(A∩B)
Given that,
A survey of 100 MBA students found that 75 owned mutual funds, 35 owned stocks and 15 owned both.
A = owned stocks
B= owned mutual funds
(a)
[tex]P(A)=\frac{\textrm{Number of students who owned a stock}}{\textrm{Total nuber of students}}[/tex]
[tex]=\frac{35}{100}[/tex]
=0.35
[tex]P(B)=\frac{\textrm{Number of students who owned a mutual funds}}{\textrm{Total nuber of students}}[/tex]
[tex]=\frac{75}{100}[/tex]
=0.75
The probability that a student owns a stocks=0.35.
The probability that a student owns a mutual funds=0.75.
The number of students who owned only a mutual fund
= Total number of students who owned a mutual fund - the number of students who owned both
=(75-15)
=60
The number of students who owned only a stock
= Total number of students who owned a stock- the number of students who owned both
=(35-15)
=20
The number students who owned either a stocks or a mutual fund or both is
= The number of students who owned only a mutual fund +The number of students who owned only a stock+the number of students who owned both
=60+20+15
=95
The number of students who owned neither a stocks nor mutual is
=100-95
=5
The probability that a student owns neither a stocks nor mutual is
= [tex]\frac{5}{100}[/tex]
=0.05
(c)
The number of students who owned either a stocks or a mutual fund is
=60+20
=80
The probability that a student owns either a stocks or a mutual fund is
[tex]=\frac{80}{100}[/tex]
=0.80
