Question

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.

Answer 1

4 has the highest probability so 4 is be most expected one.

Answer 2

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