Question

A jar contains 3 pennies, 3 nickels and 5 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.

Answer 1

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as 1 penny = ; 1 nickel = 5 ; 1 dime =10

probability X=10 =P(first coin is nickel and second coin is nickel) =(5/13)*(4/12) =0.1282

probability X=11 =P( first coin is penny and second dime +first coin is dime and second penny)

=(3/13)*(5/12)+(5/13)*(3/12)=0.1923

first	second	value of coins(x)	probabilityP(x)	xP(x)
pennny	Penny	2	0.0385	0.077
pennny	Nickel	6	0.0962	0.577
pennny	Dime	11	0.0962	1.058
Nickel	Penny	6	0.0962	0.577
Nickel	Nickel	10	0.1282	1.282
Nickel	Dime	15	0.1603	2.404
Dime	Penny	11	0.0962	1.058
Dime	Nickel	15	0.1603	2.404
Dime	Dime	20	0.1282	2.564
			total	12.000

from above expected value =12