Question

Two students are to be selected at random from a class with 10 girls and 12 boys. What is the probability that both will be girls, if selected

a) With replacement

b) Without replacement

Answer 1

a) For the first choice the total number of outcomes is 10 + 12 = 22, the number of favorable outcomes is 10; for the second choice the numbers are the same, since the choice of students is with a replacement.

$P_1=\cfrac{10}{22}\cdot\cfrac{10}{22}=\cfrac{100}{484}=\cfrac{25}{121}=0.2066.$

b) For the first choice the total number of outcomes is 10 + 12 = 22, the number of favorable outcomes is 10; for the second choice the total number of outcomes is 9 + 12 = 21, the number of favorable outcomes is 9,

$P_2=\cfrac{10}{22}\cdot\cfrac{9}{21}=\cfrac{90}{462}=\cfrac{15}{77}=0.1948.$