Question

jar contains 7 pennies, 6 nickels and 8 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the elected coins. ind the probability X- 10. Preview Find the probability X- 11.Preview Find the expected value of X.-)" Preview

Answer 1

1 penny =1 cent

1 dime =10 cents

1 nickel = 5 cents

Total number of coins in the box 7+6+8

Let N shows the event that a coin is selected, D shows the event that a dime is selected and P shows the event that a penny is selected. Since order of coins is not important so possible outcomes are:

S = { NN, PP, DD, NP, ND, PD}

Now value of X in each case is 10, 2, 20, 6, 15, 11 respectively.

Now total number of coins in the jar is: 7+6+8 = 21

Number of ways of selecting 2 coins out of 21 is C(21, 2) = 210

Now

P(X = 10) = P(NN) = C(6,2) /210 = 15 /210

P(X =2) = P(PP) = C(7,2) / 210 = 21 /210

P(X =20) = P(DD) = C(8,2) / 210 = 28 /210

P(X=6) = P(NP) = [C(7,1)*C(6,1)] / 210 = 42/210

P(X=15) = P(ND) = [C(6,1)*C(8,1)] / 210 = 48/210

P(X=11) = P(PD) = [C(7,1)*C(8,1)] / 210 = 56/210

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So,

P(X = 10) = 15 /210

P(X=11) = 56/210

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Following table shows the calculations for expected value:

X	P(X=x)	xP(X=x)
10	0.071428571	0.714285714
2	0.1	0.2
20	0.133333333	2.666666667
6	0.2	1.2
15	0.228571429	3.428571429
11	0.266666667	2.933333333
Total		11.14285714

So,