Please refer to the illustration at screenshots<dot>firefox<dot>com/jZoizoMJf8a3H0UZ/ds055uzetaobb<dot>cloudfront<dot>net
to help answer the following question:
Zeb's coin box contains 8 fair, standard coins (heads and tails) and 1 coin which has heads on both sides. He selects a coin randomly and flips it 4 times, getting all heads. If he flips this coin again, what is the probability it will be heads?
To determine the probability of getting heads on the next flip, we need to consider the possible outcomes and their corresponding probabilities.
Given that Zeb's coin box contains 8 fair, standard coins and 1 coin with heads on both sides, there are a total of 9 coins.
If Zeb selected a coin randomly, the probability of selecting the coin with heads on both sides is 1/9 because there is only one such coin in the box.
Now, Zeb flips the selected coin 4 times and gets all heads. This outcome is only possible if Zeb has selected the coin with heads on both sides. Therefore, the probability of getting all heads in 4 flips is 1/9.
If Zeb flips the coin again, the probability of getting heads will depend on the selected coin. Since we know that Zeb has already obtained all heads in the previous 4 flips, it indicates that he must have the coin with heads on both sides.
Hence, the probability of getting heads on the next flip is 1, as the selected coin has heads on both sides.
To summarize, the probability of getting heads on the next flip, given that Zeb obtained all heads in the previous four flips, is 1.