Question

a bag with 10 marbles 7 yellow marbles1 blue marble 2 red marblesa marble is chosen from the bag at random. what are the Odds in favor of choosing a yellow marble?

Answer 1

Explanation: The odd in favour of something can be calculated as follows

$Odd_{\text{in favor the event}}=\frac{probability_{\text{to happen the event}}}{probability_{\text{not to happen the event}}}$

Step 1: Once there are 7 yellow possibilities between 10 possible marbles we have that

$probability_{\text{to happen the event}}=\frac{7}{10}$

Step 2: Once there are 2 red marbles + 1 blue marble = 3 not yellow marbles between 10 marbles we have

$probability_{\text{not to happen the event}}=\frac{3}{10}$

Step 3: So the odd in favour of choosing a yellow marble is

$\begin{gathered} Odd_{\text{in favor the event}}=\frac{probability_{\text{to happen the event}}}{probability_{\text{not to happen the event}}} \\ Odd_{\text{in favor the event}}=\frac{\frac{7_{}}{10}}{\frac{3}{10}} \\ Odd_{\text{in favor the event}}=\frac{7}{10}\cdot\frac{10}{3} \\ Odd_{\text{in favor the event}}=\frac{70}{30} \\ Odd_{\text{in favor the event}}=\frac{7}{3} \end{gathered}$

Final answer: So the final answer is 7:3