Respuesta :
Given Information:
No. of Pennies = 6
No. of Nickels = 5
No. of Dimes = 6
Replacement not allowed
X represents amount in cents
Required Information:
a) P(X = 10) = ?
b) P(X = 11) = ?
c) E(X) = ?
Answer:
a) P(X = 10) = 0.073
b) P(X = 11) = 0.264
c) E(X) = 10.70
Step-by-step explanation:
1 penny is equal to 1 cent
1 nickel is equal to 5 cents
1 dime is equal to 10 cents
Total coins = 6P + 5N + 6D = 17
a) Find the probability X = 10
P(X = 10) means selecting 2 nickels so that X = 5 + 5 = 10
P(X = 10) = P(selecting 2 nickels) = 5/17*4/16 = 5/68
P(X = 10) = 0.073
b) Find the probability X = 11
P(X = 11) means selecting 1 penny and 1 dime so that X = 1 + 10 = 11
P(X = 11) = P(selecting a penny and dime) = 2*(6/17*6/16) = 9/34
P(X = 11) = 0.264
c) Find the expected value of X
We want to select 2 coins from total 17 coins
6 pennies = 6*1 = 6 cents
5 nickels = 5*5 = 25 cents
6 dimes = 6*10 = 60 cents
E(X) = 2*(6 +25 + 60)/(6 + 5 + 6)
E(X) = 2*(91/17)
E(X) = 10.70
Therefore, the expected value of X is 10.70
