Question

A box contains 3 nickels and 4 quarters. two coins are selected at random from the seven coins at the random variable X is a value of the two coins. Give the probability distribution for x.

Answer #1

3 nickels and 4 quarters

total n = 7

two coins are selected at random from the seven coins at the random variable X is a value of the two coins

X = 2 nickels

P( X = 2 nickels ) = 3C2/7C2

P( X = 2 nickels ) = 3/(7*6/2)

P( X = 2 nickels ) = 6/(7*6)

**P( X = 2 nickels ) = 1/7**

X = 2 quarters

P( X = 2 quarters ) = 4C2/7C2

P( X = 2 quarters ) = (4*3/2)/(7*6/2)

P( X = 2 quarters ) = 12/42

**P( X = 2** **quarters ) = 2/7**

X = 1 nickel and 1 quarter

P( X = 1 nickel and 1 quarter ) = 4C1*3C1/7C2

P( X = 1 nickel and 1 quarter ) = 4*3/(7*6/2)

P( X = 1 nickel and 1 quarter ) = 12/21

**P( X = 1 nickel and 1 quarter ) = 4/7**

probability distribution for x

X |
2 nickels |
1 nickel 1 quarter |
2 quarters |
Total |

P(X) |
1/7 |
4/7 |
2/7 |
1 |

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