Question

The table below shows a random sample of musicians and how they learned to play their instruments. Complete the empty cells of the table to answer the following questions.

Gender	Self-Taught	Learned in School	Private Instruction	TOTAL
Female	12	38		72
Male				58
TOTAL	31	62	37	130

1. What is the probability of randomly selecting a musician who is female?

2.What is the probability of randomly selecting a musician who is a male AND had private instruction?

3. What is the probability of randomly selecting a musician who is a female OR one that is self-taught? (Hint: be careful not to double-count individuals who meet both criteria)

4. True or False: The events of "being a female musician" and "learning music in school" are mutually exclusive.

5. The events "being a female musician" and "learning music in school" are independent events.

Answer 1

table is

gender	Self-taught	Learned in school	private Instruction	Total
male	12	38	22	72
female	19	24	15	58
total	31	62	37	130

1.

probability of randomly selecting a musician who is female is given by

2.

P(musician who is a male AND had private instruction) = no. males with private instruction/N

=15/130=0.1154

3.

P(female) =0.5538

P( self taught) =n(self taught)/N =31/130=0.2385

P(female and self taught) =n( female and self taught)/N =12/130 =0.0923

P( female or self taught) =P(female)+P( self taught) -P( female and self taught)

=0.5538+0.2385-0.0923

=0.7

4.

since there is 38 females musicians who learned music in school hence these events can not be mutually exclusive.

Hence FALSE

5.

P( female and learned in school) =n( female and learned in school)/N =38/130 =0.2923

P(female) =0.5538

P(learned in school) =n(learned in school)/N =62/130=0.4769

now

P(female)*P(learned in school) =0.5538*0.4769=0.2641 not equal to P(female and learned in school)

Hence these events are not independent.