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Consider a family with 4 children. Assume the probability that one child is a boy is 0.5 and the probability that one child is a girl is also 0.5, and that the events "boy" and "girl" are independent.

(a) List the equally likely events for the gender of the 4 children, from oldest to youngest. (Let M represent a boy (male) and F represent a girl (female). Select all that apply.)

MFFF
FFMF
FMFF
MFFM
FFFF
MMMM
MFMM
MMFM
MMMF
FFFM
MMFF
FMFM
FFMM
MFMF
FMMM
FMMF

(b) What is the probability that all 4 children are male

Respuesta :

Answer:

a) MFFF; MMFF; MMMF; MMMM; FMMM; FFMM; FFFM; FFFF; FMFM; MFMF; FFMF; FMFF; MFFM; FMMF; MMFM; MFMM; b) 1/16                                                

Step-by-step explanation:

Letting m represent boys and f represent girls, all of the events are listed.

There is 1 way to get all 4 boys out of this, MMMM.  This is out of a total of 16 events; this makes the probability 1/16.

The probability that all 4 children are male is 1/16

The equally likely event in probability means those outcomes which have similar probability to be obtained.

A list of those equally likely events is

MFFF

FFMF

FMFF

MFFM

FFFF

MMMM

MFMM

MMFM

MMMF

FFFM

MMFF

FMFM

FFMM

MFMF

FMMM

FMMF

The probability of getting all 4 children a boy = (1/2) × (1/2) × (1/2) × (1/2)

⇒ 1/16

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