a) 0.0138
b) 0.1103
Probability is the likelihood or chance that an event will occur. Mathematically;
[tex]Probability=\frac{n(E)}{n(S)}[/tex]where:
n(S) is the total outcome
n(E) is the total number of events
If a well- shuffled box contains 2 gold marbles, 6 silver marbles and 9 bronze balls, the total outcome is given as:
n(S) = 2 + 6 + 9
n(S) = 17 marbles
a) If the marbles selected are two gold marbles and replaced, the probability of selecting two gold marbles will be:
[tex]\begin{gathered} Pr(2\text{ gold marbles})=\frac{2}{17}\times\frac{2}{17} \\ Pr(2\text{ gold marbles})=\frac{4}{289} \\ Pr(2\text{ gold marbles})\approx0.0138 \end{gathered}[/tex]b) If two silver marbles are selected, the probability of selceting the first silver marble is given as:
[tex]Pr(first\text{ silver marble})=\frac{6}{17}[/tex]If the first silver marble is not replaced, the probability of picking the second one will be:
[tex]Pr(second\text{ silver marble})=\frac{6-1}{17-1}=\frac{5}{16}[/tex]The probability that they are both silver marbles if the first marble is not replaced is calculated as:
[tex]\begin{gathered} Pr(2\text{ silver marbles})=\frac{\cancel{6}^3}{17}\times\frac{5}{\cancel{16}^8} \\ Pr(2\text{ silver marbles})=\frac{15}{136} \\ Pr(2\text{ silver marbles})\approx0.1103 \end{gathered}[/tex]Hence the probability that they are both silver marbles if the first marble is not replaced is 0.1103
