First slide

Theorems of probability

Question

The sum of two positive numbers is 10. The probability that their product is greater than 20 is

Moderate

A

$\frac{1}{9}$
B

$\frac{4}{9}$
C

$\frac{5}{9}$
D

$\frac{19}{20}$

Solution

$A = S u m = 10 = {(1, 9), (9, 1), (2, 8), (8, 2), (3, 7), (7, 3), (4, 6), (6, 4), (5, 5)}$
$n (A) = 9$

$n (A \cap B) = 5$

$P (\frac{B}{A}) = \frac{5}{9}$

The probability that their product is greater than 20 is $\frac{5}{9}$

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