If necessary consult a list of formulas An urn contains red

(If necessary, consult a list of formulas.)

An urn contains red balls and white balls. If Frank chooses balls at random from the urn, what is the probability that he will select red balls and white balls? Round your answer to decimal places. (If necessary, consult a list of formulas.)

Solution

According to condition ,

The number of ways of choosing 5 reds from 10 is ₁₀C₅=252 the number of ways of choosing 2 whites from 3 is ₃C2=3

So the number of possible successes is 3*252=756 i.e each one of these combinations will have 5 red and 2 white balls. Now the total number of ways of choosing 7 balls out of 13 is ₁₃C₇=1716 so the probability is P=# successes/total number= 756/1716=0.441   answer