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

Step-by-step 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}}=(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}}=(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}}{(3)/(10)} \\ Odd_{\text{in favor the event}}=(7)/(10)\cdot(10)/(3) \\ Odd_{\text{in favor the event}}=(70)/(30) \\ Odd_{\text{in favor the event}}=(7)/(3) \end{gathered}`

Final answer: So the final answer is 7:3