Question

Suppose you like to keep a jar of change on your desk. Currently, the jar contains the following: 17 Pennies 10 Dimes 19 Nickels 23 Quarters What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a penny

Answer 1

Answer:

0.0688 = 6.88% probability that you reach into the jar and randomly grab a nickel and then, without replacement, a penny.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Probability of grabbing a nickel:

19 nickels out of 17+10+19+23 = 69 coins, so:

$P(A) = \frac{19}{69}$

Probability of grabbing a penny, considering the first coin grabbed was a nickel:

17 pennies out of 68 coins. So

$P(B|A) = \frac{17}{68} = \frac{1}{4}$

What is the probability that you reach into the jar and randomly grab a nickel and then, without replacement, a penny?

$P(A \cap B) = P(A)P(B|A) = \frac{19}{69} \times \frac{1}{4} = \frac{19}{69*4} = 0.0688$

0.0688 = 6.88% probability that you reach into the jar and randomly grab a nickel and then, without replacement, a penny.