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Question

There are four nickels and four dimes in your pocket. You randomly pick a coin out of your pocket and place it on a counter. Then you randomly pick another coin.  Find the probability the first coin is a nickel and the second coin is a dime.

Answer 1

The probability of an individual event, or P(E), occurring is determined by dividing the number of desired outcomes by the total number of outcomes. The probability of two events occurring is determined by finding the product (multiplying) the individual event probabilities.

Step 1: Find the probability for the first draw.

Pretty straightforward, calculate by using the definition of probability of an event occurring.

P(E1) = Probability of drawing a nickel for first draw

P(E1) = number of nickels to choose from on first draw / total number of coins available on first draw

P(E1) = 4/8 = 1/2 = 0.5

Step 2: Find the probability for the second draw.

The second draw is slightly different because you need to remember that you have one less nickel. This does not affect the numerator, but it does affect the denominator.

P(E2) = Probability of drawing a dime for the second draw

P(E2) = number of dimes to choose from / total number of coins available for the second draw

P(E2) = 4/7

Step 3: Multiply the individual probabilities to find the total probability of drawing a nickel first and a dime second.

P(E1,E2) = P(E1) x P(E2)

P(E1,E2) = (1/2) x (4/7)

P(E1,E2) = 2/7