Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following:

13Pennies

15 Dimes

29 Nickels

26 Quarters

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What is the probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel? Express your answer as a fraction or a decimal number rounded to four decimal places.

Answer 1

Number of Pennies =13

Number of Dimes = 15

Number of Nickels =29

Number of Quarters = 26

Total number of coins in the jar = 13+15+29+26=83

probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel

A : Event of grabbing a dime first

B : Event of grabbing a nickel in the second(without replacement)

probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel

= P(A and B) = P(A) P(B|A)

P(A) = Number of dimes in the jar / Total number of coins = 15/83

Given that first grab was a dime, number of coins left in the jar = 82; Number of nickels in the jar are intact i.e  29

P(B|A) = Probability grabbing a nickel in the second(without replacement) given that first grab was a Dime

= Number of nickels in the jar / Total number of number of coins left in the jar =29/82

P(A and B) = P(A) P(B|A) = (15/83)(29/82) = 285/6806

probability that you reach into the jar and randomly grab a dime and then, without replacement, a nickel = 285/6806 =0.0419