Question

20. An urn contains n white counters numbered 1 through n, n black counters numbered 1 through n, and n red counter numbered 1 through n. If two counters are to be drawn at random without replacement, what is the probability that both counters will be of the same color or bear the same number?

Answer 1

Answer:

Step-by-step explanation:

• Given white = n - counters

• red = n-counters

• black = n - counters

• total = 3n - counters

choosing randomly a counter of any color; n -1 counters will be left of the same color, total = 3n - 1 counters left

• hence, probability of both same color of counters = n-1/3n-1

• to get the probability that both counters are of he same number ;

we are told that ; n white counters numbered 1 through n, n black counters numbered 1 through n, and n red counter numbered 1 through n

• similarly, choosing a counter randomly of the same number = 2 counters will be left of same number and total left will be 3n-1

• as such probability that both counters are of the same color = 2/3n-1

• hence, probability of the same color or same number = n-1/3n-1 + 2/3n-1 = n+1/3n-1