GKT101: General Knowledge for Teachers – Math

1. (b) and (c) are dependent. The probability of the second event occurring depends on the first event occurring.

2. (a) and (c) are dependent. The probability of the second event occurring depends on the first event occurring.

3. The probability can be calculated as follows: $\dfrac{27}{37} \times \dfrac{10}{36}=\dfrac{270}{1332}=\dfrac{15}{74}=0.203=20.3 \%$

4. The probability can be calculated as follows: $\dfrac{10}{37} \times \dfrac{27}{36}=\dfrac{270}{1332}=\dfrac{15}{74}=0.203=20.3 \%$

5. The probability of drawing 2 face cards one after the other without replacement can be calculated as follows: $\dfrac{12}{52} \times \dfrac{11}{51}=\dfrac{132}{2652}=\dfrac{11}{221}=0.050=5.0 \%$

6. The probability can be calculated as follows: $\dfrac{13}{50} \times \dfrac{3}{49}=\dfrac{39}{2450}=0.016=1.6 \%$

7. The coins that are not dimes are quarters, nickels, and pennies. Therefore, the probability can be calculated as follows:

$\begin{gathered}\text { quarters }+\text { nickels }+\text { pennies }=3+13+27=43 \\\dfrac{43}{50} \times \dfrac{42}{49}=\dfrac{1806}{2450}=0.737=73.7 \%\end{gathered}$

8. The doughnuts that are not jelly are glazed and plain. Therefore, the probability can be calculated as follows:

$\dfrac{5}{6} \times \dfrac{4}{5} \times \dfrac{3}{4} \times \dfrac{2}{3} \times \dfrac{1}{2}=\dfrac{120}{720}=\dfrac{1}{6}=0.167=16.7 \%$

9. The prime numbers from 1 through 20 are $2,3,5,7,11,13,17$, and 19 . Therefore, the probability can be calculated as follows: $\dfrac{8}{20} \times \dfrac{7}{19}=\dfrac{56}{380}=\dfrac{14}{95}=$ $0.147=14.7 \%$

10. For Steve's cards to consist of a heart and a diamond, he can draw a heart and then a diamond or a diamond and then a heart. Therefore, the probability can be calculated as follows:

$\dfrac{13}{52} \times \dfrac{13}{51}+\dfrac{13}{52} \times \dfrac{13}{51}=\dfrac{169}{2652}+\dfrac{169}{2652}=\dfrac{338}{2652}=\dfrac{169}{1326}=0.127=12.7 \%$