Question

Chi Kong has five pennies and five nickels in his pocket if he picks two coins in a row which is more likely that he will pick out two pennies or one penny and a nickel?

Answer 1

He has 5 pennies and 5 nickels in his pocket.

If he pick two coins in a row, we have to compare the probabilities of getting two pennies or one penny and one nickel. We will assume that there is no reposition: the coin that is drawn is not put again in the pocket.

Probability of getting two pennies:

For the first draw, it has p=0.5 (50% of chances) of getting a penny, as there are 10 coins and 5 of them are pennies.

Then, for the second draw there is p=4/9=0.44 chances of getting a penny, as one has already been picked.

Then, the probability of getting two pennies in a row is:

`P(2\text{ pennies})=0.5\cdot0.44=0.22`

Probability of getting one penny and one nickel:

For the first draw, we can get pennies or nickels. Both of them are valid, so we will have a probability of p=1 for the first draw.

Then, for the second draw, we have to pick the other category: if we had a penny in the first draw, we should get a nickel in the second one and, if we had a nickel in the first draw, we should get a penny in the second draw.

In both cases, there will be 5 coins of the other category out of the 9 remaining coins.

Then, the probability of success in the second draw is p=5/9=0.55.

Then, the probability of getting one nickel and one penny is:

`P(1N\&1P)=1\cdot0.55=0.55`

Answer: it is more likely that he will pick out one penny and a nickel.