NUM_COINS coins in a bag.
NUM_UNFAIR_COINS of them are unfair in that they have a
PERCENT_CHANCE_UNFAIR_HEADS\% chance of coming up heads when flipped (the rest are fair coins). You randomly choose one coin from the bag and flip it
What is the probability, written as a percentage, of getting
NUM_FLIPS heads? Round your answer to the nearest hundredth of a percent.
You can only pick a fair coin or pick an unfair coin. There is no other outcome.
What chance do you have of picking an unfair coin? How about a fair coin?
An unfair coin occurs
UNFAIR_COIN_FRACTION_STRING of the time.
A fair coin occurs the rest of the time, or
FAIR_COIN_FRACTION_STRING of the time.
UNFAIR_COIN_FRACTION_STRING of the time that you pick an unfair coin,
what is the chance of flipping
NUM_FLIPS heads using that unfair coin?
The chance is
Now, then, your chance of both picking the unfair coin and also flipping
NUM_FLIPS heads--the chance that both these events occur--is what?
UNFAIR_COIN_FRACTION_STRING \times UNFAIR_HEADS_DECIMAL_FORMULA.
Now, the other possibility, picking the fair coin and flipping
NUM_FLIPS heads is what?
FAIR_COIN_FRACTION_STRING \times FAIR_HEADS_DECIMAL_FORMULA.
How do you combine these two mutually exclusive events to find the chance that either occurs?
Add them! So your answer is
UNFAIR_COIN_FRACTION_STRING \times UNFAIR_HEADS_DECIMAL_FORMULA+
FAIR_COIN_FRACTION_STRING \times FAIR_HEADS_DECIMAL_FORMULA, or