Probability of a male not completing = 4 / (11+4) = 4/15
Probability of a female not completing = 2 / (12+2) = 2/14 = 1/7
Twice the female probability = 2 * (1/7) = 2/7
Comparing the probabilities: 4/15 ≈ 0.267 and 2/7 ≈ 0.286.
Since 0.267 is very close to 0.286, the data supports her view.
Alternatively, comparing proportions:
Proportion of males not completing = 4/15.
Proportion of females not completing = 2/14.
Twice the female proportion is 2 * (2/14) = 4/14.
4/15 is nearly the same as 4/14, so the statement is supported.
To check Miss Wardle's statement, we need to compare the conditional probabilities.
First, find the total number of males: 11 + 4 = 15.
The probability of a male not completing is P(not complete | male) = 4/15.
Next, find the total number of females: 12 + 2 = 14.
The probability of a female not completing is P(not complete | female) = 2/14 = 1/7.
Miss Wardle says males are "nearly twice as likely" as females. Let's double the female probability:
2 * P(not complete | female) = 2 * (1/7) = 2/7.
Now we compare the male probability (4/15) with twice the female probability (2/7).
To compare them easily, find a common denominator or convert to decimals:
4/15 ≈ 0.267
2/7 ≈ 0.286
Since 0.267 is very close to 0.286, the data supports her view.
Expert