Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X denote the sum of the numbers. Find the expected value of the sum.
Answers
Answer:
3
Step-by-step explanation:
Two cards are drawn at random from a box which contains 5 cards numbered 1, 1, 2, 2 and 3. Let X denote the sum of the numbers. Find the expected value of the sum
Three cases:
First card 1 , 2 or 3
Probability of 1 = 2/5
Probability of 1 = 1/4 Probability of 2 = 2/4 Probability of 3 = 1/4
Probability of sum 2 (1 + 1) = (2/5)(1/4) = 1/10
Probability of sum 3 (1 + 2)= (2/5)(2/4) = 1/5
Probability of sum 4 (1+3)= (2/5)(1/4) = 1/10
Probability of 2 = 2/5
Probability of 1 = 2/4 Probability of 2 = 1/4 Probability of 3 = 1/4
Probability of sum 3 (2 + 1) = (2/5)(2/4) = 1/5
Probability of sum 4 (2 + 2) = (2/5)(1/4) = 1/10
Probability of sum 5 (2 + 3) = (2/5)(1/4) = 1/10
Probability of 3 = 1/5
Probability of 1 = 2/4 Probability of 2 = 2/4
Probability of sum 4 (2 + 2) = (1/5)(2/4) = 1/10
Probability of sum 5 (2 + 3) = (1/5)(2/4) = 1/10
Probability of sum 2 = 1/10
Probability of sum 3 = 1/5 + 1/5 = 2/5
Probability of sum 4 = 1/10 + 1/10 + 1/10 = 3/10
Probability of Sum 5 = 1/10 + 1/10 = 1/5
Max probability of sum 3 = 2/5
so expected value of the sum = 3