Question

For the accompanying table, is the sum of the values of P(x)

equal to 1, as required for a probability distribution? Does the table describe a probability distribution?

Number of Girls x	P(x)
0	0.063
1	0.250
2	0.375
3	0.250
4	0.063

Short answer

The distribution of x describes a probability distribution.

Step-by-step solution

Given information

The probability for the number of girls is provided.

State the requirements of the probability distribution

The two characteristics of the probability distribution are as follows.

• All probabilities must be between 0 and 1.
• The sum of all probabilities must be 1.

Check the sum of the probabilities

Each probability value is between 0 and 1.

The sum of the probabilities is computed as

$$\begin{gathered} P\left(x=0\right)+P\left(x=1\right)+P\left(x=2\right)+P\left(x=3\right)+P\left(x=4\right)=0.063+0.25+0.375+0.25+0.063 \\ =1.001 \end{gathered}$$

The difference of 0.001 from 1 can be inferred to be a round-off error in probability values.

Thus, it can be concluded that the sum of the probability is not 1, but it is close enough to 1.

Comment for the probability distribution of x

As the sum can be concluded to be close to 1 and the difference can be explained by the round-off errors in probabilities, it can be inferred that the table provided in the given scenario describes a probability distribution.