A jar contains 6 pennies, 5 nickels and 6 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Find the probability X = 10. Find the probability X = 11. Find the expected value of X.

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) = ?

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

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step-by-step explanation:

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.