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