Math  /  Data & Statistics

QuestionYou select a family with three children. If MM represents a male child and FF a female child, the set of equally likely outcomes for the children's sexes is \{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}. Assuming that the probability of a male or female birth is 0.5 , find the probability of selecting a family with i) Exactly one female child? ii) Exactly two male children? i) 0.375 , ii) 0.125 i) 0.375 , ii) 0.375 i) 0.125 , ii) 0.375 i) 0.125 , ii) 0.125

Studdy Solution

STEP 1

1. Each child is equally likely to be male or female, with a probability of 0.5 for each.
2. The outcomes are independent of each other.
3. The sample space for the outcomes is \{MMM, MMF, MFM, MFF, FMM, FMF, FFM, FFF\}.

STEP 2

1. Calculate the probability of exactly one female child.
2. Calculate the probability of exactly two male children.

STEP 3

Identify the outcomes with exactly one female child:
The outcomes are: \{MMF, MFM, FMM\}.

STEP 4

Count the number of favorable outcomes for exactly one female child:
There are 3 favorable outcomes.

STEP 5

Calculate the probability of exactly one female child:
The total number of outcomes is 8. Thus, the probability is:
P(exactly one female)=38=0.375 P(\text{exactly one female}) = \frac{3}{8} = 0.375

STEP 6

Identify the outcomes with exactly two male children:
The outcomes are: \{MMF, MFM, FMM\}.

STEP 7

Count the number of favorable outcomes for exactly two male children:
There are 3 favorable outcomes.

STEP 8

Calculate the probability of exactly two male children:
The total number of outcomes is 8. Thus, the probability is:
P(exactly two males)=38=0.375 P(\text{exactly two males}) = \frac{3}{8} = 0.375
The probabilities are: i) Exactly one female child: 0.375 \boxed{0.375} ii) Exactly two male children: 0.375 \boxed{0.375}

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