Question

A frequency distribution for the number of Nobel prize winners by the country for the years $1901-2001$ is given below:

Country	Winners
United States	$261$
United Kingdom	$79$
Germany	$61$
France	$28$
Soviet Union	$11$
Japan	$7$
Other countries	$57$

Suppose that a Nobel Prize recipient during the period $1901-2001$ is selected at random.

Find the probability that Nobel prize winner is from

a) Soviet Union

b) Either France or Germany

c) Any country other than the United States

Answer 1

Finding the required probability:

The total number of Nobel Prize recipients are,

$$\begin{gathered} =261+79+61+28+11+7+57 \\ =504 \end{gathered}$$

The probability that the recipient is from the Soviet Union,

$$\begin{gathered} =\frac{\mathrm{Favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{\mathrm{Number}\mathrm{of}\mathrm{recipients}\mathrm{from}\mathrm{Soviet}\mathrm{Union}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{recipients}} \\ =\frac{11}{504} \end{gathered}$$

The probability that the recipient is from either France or Germany,

$$\begin{gathered} =\frac{\mathrm{Favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{\mathrm{Number}\mathrm{of}\mathrm{recipients}\mathrm{from}\mathrm{Germany}\mathrm{and}\mathrm{France}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{recipients}} \\ =\frac{61+28}{504} \\ =\frac{89}{504} \end{gathered}$$

The probability that the recipient is from any country other than the US states,

$$\begin{gathered} =\frac{\mathrm{Favourable}\mathrm{outcomes}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{outcomes}} \\ =\frac{\mathrm{Number}\mathrm{of}\mathrm{recipients}\mathrm{from}\mathrm{all}\mathrm{states}\mathrm{other}\mathrm{than}\mathrm{United}\mathrm{States}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{recipients}} \\ =\frac{504-261}{504} \\ =\frac{243}{504} \end{gathered}$$

Hence, the correct answers are a) $\frac{11}{504}$b) $\frac{89}{504}$ c) $\frac{243}{504}$