Standard +0.3 This is a straightforward probability question requiring calculation of P(X≥2) where X follows a hypergeometric distribution. Students need to identify the favorable outcomes (houses numbered 16-24, which is 5 houses) and calculate P(X=2) + P(X=3) using combinations. While it requires careful counting and organization, it's a standard application of basic probability principles with no conceptual surprises, making it slightly easier than average.
2 The 12 houses on one side of a street are numbered with even numbers starting at 2 and going up to 24 . A free newspaper is delivered on Monday to 3 different houses chosen at random from these 12. Find the probability that at least 2 of these newspapers are delivered to houses with numbers greater than 14.
12, 11, 10 seen or implied in denominator; Mult a prob by \(_nC_r\) or \(_nC_1\) oe
\(= \frac{5}{11}\) (0.364)
A1 [4]
Correct answer
OR \(\frac{(_5C_1) + (_6C_2 \times _7C_1)}{_{12}C_3}\)
M1
\(_nC_i\) seen added in numerator
M1
\(_nC_2\) seen mult alone or in numerator
M1
\(_{12}C_3\) seen in denom
A1
Correct answer
$P(\text{at least } 2) = P(2, 3) \text{ or } 1 - P(0, 1)$ | M1 | Summing, or $1-$, two different three-factor prob expressions, $_nC_r$ not needed
$= \frac{5}{12} \times \frac{4}{11} \times \frac{7}{10} \times _3C_2 + \frac{5}{12} \times \frac{4}{11} \times \frac{3}{10}$ | M1 | 12, 11, 10 seen or implied in denominator; Mult a prob by $_nC_r$ or $_nC_1$ oe
$= \frac{5}{11}$ (0.364) | A1 [4] | Correct answer
OR $\frac{(_5C_1) + (_6C_2 \times _7C_1)}{_{12}C_3}$ | M1 | $_nC_i$ seen added in numerator
| M1 | $_nC_2$ seen mult alone or in numerator
| M1 | $_{12}C_3$ seen in denom
| A1 | Correct answer
2 The 12 houses on one side of a street are numbered with even numbers starting at 2 and going up to 24 . A free newspaper is delivered on Monday to 3 different houses chosen at random from these 12. Find the probability that at least 2 of these newspapers are delivered to houses with numbers greater than 14.
\hfill \mbox{\textit{CAIE S1 2013 Q2 [4]}}