We use following steps for Probability of red and white balls -
Step 1: First of all, we find out Sample Space of given situation means here we find out how many balls are stored in a bag -
3 + 6 + 7 = 16,
So, there are 16 balls are stored in a bag.
Step 2: Now we how many cases we have to retrieve from given bag, there are 2 balls we have to retrieve in one time. So, total case are-
16C2 = (16 * 15) / (2 * 1),
= 120.
Therefore, there are 120 total cases.
Step 3: Now we find out how many ways is there for getting red ball in that bag-
3C1 are the total number of ways for evaluating a red ball in that bag means,
3C1 = 3,
So, there are 3 ways for getting a red ball from that bag.
Step 4: Now we find out how many ways is there for getting blue ball in that bag-
7C1 are the total number of ways for evaluating a red ball in that bag means.
7C1 = 7,
So, there are 7 ways for getting a red ball from that bag.
Step 5 : Now we calculate probability of total number of favorable cases by using multiplication theorem on probability-
Total number of favorable cases
= number of ways to getting red ball * number of ways to getting blue ball
= 3 * 7
= 21
So, total number of favorable cases is 21.
Now we calculate probability that two balls drawn are red and white
= total favorable case / total sample space
= 21 / 120
= 7 / 40
Therefore, probability of two balls drawn are red and white is 7 / 40.