Question

To the right are the outcomes that are possible when a couple has three children. Refer to that​ list, and find the probability of each event. a. Among three​ children, there are exactly 2 boys. b. Among three​ children, there are exactly 3 boys. c. Among three​ children, there is exactly 1 boy.

Answer 1

Answer:

The probabilities are 3/8, 1/8 and 3/8 respectively

Step-by-step explanation:

The sample space for the provided case can be written as:

S= {(bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg)}

Here, boy child is denoted by "b" and girl child by "g".

Total number of outcomes are 8.

Number of outcomes that show exactly boys = 3.

Number of outcomes that show exactly 3 boys = 1

Number of outcomes that show exactly 1 boy = 3.

Thus, the required probabilities can be calculated as:

(a)

$\\P( Exactly 2 boys) =\frac{3}{8}$

(b)

$P( Exactly 3 boys) =\frac{1}{8}$

(c)

$P(Exactly 1 boy)= \frac{3}{8}$

Thus, the required probabilities are 3/8, 1/8 and 3/8 respectively.