Question

A penny bank contains 1 quarter, 4 dimes, and 2 nickels. You reach in and randomly pull out two coins. Let X be the random variable representing the value of the coins you pull out in cents (e.g. a dime and a nickel would make X=15). Construct a probability distribution for X.

How many values of *X* are possible?

Answer #1

1 quarter=25 cent

1 dime =10 cents

1 nickel = 5 cents

Total number of coins in the box 1+4+2=7

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

S = { NN, DD, NQ, ND, DQ}

The value of X in above cases is 10, 20, 30, 15, 35. Number of ways of seelcting 2 coins out of 7 is C(7,2) = 21. Since there are 2 nickels so

P(X = 10) = P(NN) = C(2,2) / 21 = 1/21

Since there are 4 Dimes so *

P(X = 20) = P(DD) = C(4,2) / 21 = 6/21

Likewise *

P(X = 30) = P(NQ) = [C(2,1)*C(1,1) ] / 21 = 2 / 21

P(X = 15) = P(ND) = [C(2,1)*C(4,1) ] / 21 = 8 / 21

P(X = 35) = P(DQ) = [C(1,1)*C(4,1) ] / 21 = 4 / 21

Following table shows the pdf:

X | P(X=x) |

10 | 1/21 |

15 | 8/21 |

20 | 6/21 |

30 | 2/21 |

35 | 4/21 |

Suppose a bag contains 2 quarters, 1 dime, 5 nickels, and 3
pennies. If you randomly select one coin out of the bag, what is
the probability that it is a nickel? P(N) = ________ If you
randomly select one coin out of the bag, what is the probability it
is not a quarter? P(Q) = ________ If you select two coins with
replacement, what is the probability of picking a dime (D1) and
then a penny (P2)? Reminder: Show...

A jar contains 4 pennies, 2 nickels and 4 dimes. A child selects
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A
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coins at random without replacement from the jar. Let x represent
the amount in cents of the selected coins.
Find the probability X=10
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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.

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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..........................
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Find the expected value of X. ...........................

a jar contains 3 pennies, 8 nickels and 7 dimes. a
child selects 2 coins at random without replacement from the jar.
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