Question

A bag contains 4 coins of Rs 5 and 6 coin of Rs.2, a coin is drawn at random, the expected gain is​

Answer 1

The expected gain is  Rs 3.2  if a bag contains 4 coins of Rs 5 and 6 coin of Rs.2 and a coin is drawn at random

Given:

• A bag contains 4 coins of Rs 5 and 6 coin of Rs.2
• A coin is drawn at random

To Find:

• Expected Gain

Solution:

• Expected Value   ∑X.P(X)
• Probability of an event  = n(E)/n(S)  
• n(E) = number of possible outcome of event
• n(S) = number of possible sample space outcome

Step 1:

Find Total coins

4 + 6 = 10

Step 2:

Find probability of Rs 5 coins

P(5) = Rs 5 coins / Total Number of coins

P(5)  = 4/10  = 0.4

Step 3:

Find probability of Rs 2 coins

P(5) = Rs 2 coins / Total Number of coins

P(2)  = 6/10  = 0.6

Step 4:

Find the expected gain

X           P(X)       X.P(X)

5           0.4           2

2           0.6           1.2

           ∑X.P(X)      3.2

Hence, the expected gain is  Rs 3.2