The probability that a student selected at random is a male is 0.48, and a student likes statistics is 0.35. The probability of selected at random a female who likes statistics is 0.25.

i. Construct a contingency table based on the information given above.

ii. What is the probability that a student selected at random is a male and likes statistics;

iii. What is the probability that a student selected at random is a female or likes statistics.

### Solution

i. The probability that a student selected at random is a male is 0.48. Then the probability that a student selected at random is a female is (1-0.48 )= 0.52.

So if we assume that there are total 100 students, then 48 are male and 52 are female.

The probability that a student selected at random likes statistics is 0.35, so the probability that a student selected at random does not like statistics is (1-0.35) = 0.65.

Thus total number of students who likes statistics is 35 and those who does not like statistics is 65.

The probability of selected at random a female who likes statistics is 0.25. That is number of female students who likes statistics is 25.

. | Male | Female | Total |
---|---|---|---|

Like Statistics | 10 (=35-25) | 25 | 35 |

Does not like Statistics | 38 (=48-10) | 27 (=52-25) | 65 |

Total | 48 | 52 | 100 |

ii. The probability that a student selected at random is a male and likes statistics is

` $$ \begin{aligned} P(\text{Male}\cap \text{Like Statistics}) &= \frac{10}{100}\\ &= 0.10 \end{aligned} $$ `

iii. The probability that a student selected at random is a female or likes statistics is

` $$ \begin{aligned} P(\text{Female}\cup \text{Like Statistics}) &= P(\text{Female}) + P(\text{Like Statistics}) - P(\text{Female}\cap \text{Like Statistics})\\ &=\frac{52}{100}+ \frac{35}{100}- \frac{25}{100}\\ &= \frac{62}{100}\\ &=0.62 \end{aligned} $$ `

#### Further Reading

- Statistics
- Descriptive Statistics
- Probability Theory
- Probability Distribution
- Hypothesis Testing
- Confidence interval
- Sample size determination
- Non-parametric Tests
- Correlation Regression
- Statistics Calculators