Question

Consider the following game that is played with a fair coin (a coin that is equally likely to land heads up as tails up). To play the game you flip the coin either once or twice. If the first fip is heads, you get a black chip and the game ends (you don't flip a second time). If the first flip is tails, then you get a red chip and you flip again. If the second flip is heads, you get a black chip. If it is tails, you get a red chip. Make some guesses before you do any calculations. What is the probability of getting a black chip when you play the game?

Answer 1

The probability of getting a black chip in the coin flip game is 75%, considering the two possible ways of obtaining a black chip either by getting heads on the first flip or tails on the first flip followed by heads on the second flip.

Step-by-step explanation:

Probability of Getting a Black Chip

To calculate the probability of getting a black chip in the game, we need to consider each possible outcome and its associated probability. There are two possible ways to get a black chip: either the first coin flip is heads, or the first is tails followed by a second flip that is heads. The probability of flipping heads on a fair coin is 0.5. Therefore, the probability of getting a black chip on the first flip (heads) is 0.5. If the first flip is tails (also with a probability of 0.5), there's again a 0.5 chance that the second flip will be heads. So, the probability of getting a black chip after the first flip is tails is 0.5 * 0.5 = 0.25.

Now, we add the probabilities of the two separate ways to obtain a black chip together:

• First flip heads: 0.5
• First flip tails, second flip heads: 0.25

The total probability of getting a black chip is the sum of the above probabilities: 0.5 + 0.25 = 0.75. Therefore, there is a 75% chance of getting a black chip when playing the game.