You have 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 NUM_FLIPS
times.
What is the probability, written as a percentage, of getting NUM_FLIPS
heads? Round your answer to the nearest hundredth of a percent.
ANSWER
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.
For that 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 UNFAIR_HEADS_PERCENT_FORMULA
, or
UNFAIR_HEADS_DECIMAL_FORMULA
.
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?
It is UNFAIR_COIN_FRACTION_STRING \times UNFAIR_HEADS_DECIMAL_FORMULA
.
Now, the other possibility, picking the fair coin and flipping NUM_FLIPS
heads is what?
It is 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
ANSWER\%
.