Question

bag of coins contains two quarters 5 dimes 3 nickels and 4 pennies if two coins are randomly chosen from the bag one after the other not replaced and if the total value of the chosen coins is $0.26 what is the probability that a third coin randomly chosen from the back will be a penny

Answer 1

A - the total value of the first two chosen coins is $0.26
B - third chosen coin is a penny


`P(B|A)=(P(A \cap B))/(P(A))\\\\ |\Omega|=14\cdot13=182\\ |A|=2\cdot4\cdot2!=16\\ |A \cap B|=16\cdot3=48\\\\ P(A \cap B)=(48)/(182\cdot12)=(2)/(91)\\ P(A)=(16)/(182)=(8)/(91)\\\\ P(B|A)=((2)/(91))/((8)/(91))=(2)/(91)\cdot(91)/(8)=(1)/(4)`