Question

The following table shows number of males and females of a locality in different age groups.

$\begin{array}{cccc}Ageinyears& 10-20& 21-50& Above50\\ Male& 15& 16& 9\\ Female& 8& 20& 12\end{array}$

If a person is selected at random, then which of the following options is/are true?

• A. The probability of getting a male aged 10-20 is $\frac{3}{16}$
• B. The probability of getting a female aged 10-20 is $\frac{13}{16}$
• C. The probability of getting a female is $\frac{1}{3}$
• D. The probability of getting a female is $\frac{1}{2}$

Answer 1

Answer: (A), (D)

The correct options are
A

The probability of getting a male aged 10-20 is $\frac{3}{16}$

D

The probability of getting a female is $\frac{1}{2}$

Total number of people in the given locality = 15 + 16+ 9 + 8 + 20 + 12

= 80

Total number of females = 8 + 20 + 12

= 40

Number of males with age 10-20 = 15
Number of females with age 10-20 = 8

$\text{Probability to get a male aged 10-20}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

$=\frac{\text{Number of males with age 10-20}}{\text{Total number of people in the given locality}}$

= $\frac{15}{80}$

= $\frac{3}{16}$

$\text{Probability to get a female aged 10-20}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

$=\frac{\text{Number of females with age 10-20}}{\text{Total number of people in the given locality}}$

= $\frac{8}{80}$

= $\frac{1}{10}$

$\text{Probability to get a female}=\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}$

$=\frac{\text{Number of females}}{\text{Total number of people in the given locality}}$

= $\frac{40}{80}$

= $\frac{1}{2}$