Question

Two urns both contain green balls and red balls. Urn I contains 6 green balls and 4 red balls and Urn II contains 8 green balls and 7 red balls. A ball is drawn from each urn. What is the probability that both balls are red? a. 14/75 b. 7/25 c. 2/75 d. 7/150

Answer 1

Option A is the correct answer.

Explanation:

Probability is the ratio of number of favorable outcome to total number of outcomes,

Urn I contains 6 green balls and 4 red balls and Urn II contains 8 green balls and 7 red balls.

`\texttt{Probability of drawing red ball from Urn 1= }\frac{\texttt{Number of red balls in Urn 1}}{\texttt{Number of balls in Urn 1}}\\\\\texttt{Probability of drawing red ball from Urn 1= }(4)/(4+6)=(4)/(10)\\\\\texttt{Probability of drawing red ball from Urn 1= }(2)/(5)`

Urn II contains 8 green balls and 7 red balls.

`\texttt{Probability of drawing red ball from Urn 2= }\frac{\texttt{Number of red balls in Urn 2}}{\texttt{Number of balls in Urn 2}}\\\\\texttt{Probability of drawing red ball from Urn 2= }(7)/(8+7)=(7)/(15)\\\\\texttt{Probability of drawing red ball from Urn 2= }(7)/(15)`

Probability that both balls are red if a ball is drawn from each urn = Probability of drawing red ball from Urn 1 x Probability of drawing red ball from Urn 2

`\texttt{Probability that both balls are red if a ball is drawn from each urn = }(2)/(5)* (7)/(15)\\\\\texttt{Probability that both balls are red if a ball is drawn from each urn = }(14)/(75)`

Option A is the correct answer.

Answer 2

From the first urn, since there are 10 balls and 4 of which are red then, the update in the expanssion.

P1 = 4/6 = 2/3

In the second urn, the probability of picking white is 7/15.
Pf = (2/3)(7/15) = 21/81