Question

A bag contain 4 blue and 5 green balls another bag contain 3 blue and 7 green balls if one ball is drawn from each bag, what is the probability that two balls are of the same colour.

Answer 1

p( getting two balls of same colour) = 7

Answer 2

Answer:

$\textrm{probability of drawing two balls same color from each bag}= \dfrac{47}{90}$

Explanation:

Number of blue balls in first bag = 4

Number of green ball in first bag = 5

total number of ball in first bag = 9

$\textrm{probability of drawing a blue ball from first bag\ }=\ \dfrac{number\ of\ the\ blue\ ball\ in\ first\ bag}{total\ number\ of\ ball\ in\ the\ first\ bag}$

                                                    $=\ \dfrac{4}{9}$

$\textrm{probability of drawing a green ball from first bag}\ =\ \dfrac{number\ of\ the\ green\ ball\ in\ first\ bag}{total\ number\ of\ ball\ in\ the\ first\ bag}$

                                                  $=\ \dfrac{5}{9}$

number of blue ball in second bag = 3

number of green ball in second bag = 7

total number of ball in second bag = 10

$\textrm{probability of drawing a blue ball from second bag}\ =\ \dfrac{number\ of\ the\ blue\ ball\ in\ second\ bag}{total\ number\ of\ the\ ball\ in\ second\ bag}$

                                                    $=\ \dfrac{3}{10}$

$\textrm{probability of drawing a green ball from second bag}\ =\ \dfrac{number\ of\ green\ ball\ in\ second\ bag}{total\ number\ of\ ball\ in\ second\ bag}$

                                                   $=\ \dfrac{7}{10}$

$\textrm{probability of drawing same color of ball from each bag}\ =\ \dfrac{4}{9}\times \dfrac{3}{10}\ +\ \dfrac{5}{9}\times \dfrac{7}{10}$

                                                          $=\dfrac{47}{90}$

Hence, the probability of drawing same color of ball from each bag is $\dfrac{47}{90}$