When you flip a biased coin the probability of getting a tail is 0.6.
How many times would you expect to get tails if you flip the coin 320 times?
Can you find .6(320) ?
To find out how many times we can expect to get tails when flipping a coin 320 times with a probability of getting tails of 0.6, we can use the concept of expected value.
The expected value (denoted by E(X)) is calculated by multiplying each possible outcome by its probability, and then summing up all these products.
In this case, the possible outcomes are either getting a tail or not getting a tail (getting a head). The probability of getting a tail is 0.6, while the probability of getting a head is 1 - 0.6 = 0.4.
Let's use the formula for expected value:
E(X) = (Probability of Outcome 1 * Outcome 1) + (Probability of Outcome 2 * Outcome 2) + ...
In this case:
E(X) = (0.6 * Number of Tails) + (0.4 * Number of Heads)
Since there are only two possible outcomes (tails or heads), we can simplify it to:
E(X) = 0.6 * Number of Tails + 0.4 * (Total Flips - Number of Tails)
Now, plug in the values:
E(X) = 0.6 * Number of Tails + 0.4 * (320 - Number of Tails)
We want to find the expected number of tails, so let's solve for Number of Tails:
E(X) = 0.6 * Number of Tails + 0.4 * (320 - Number of Tails)
Expanding the equation:
E(X) = 0.6 * Number of Tails + 0.4 * 320 - 0.4 * Number of Tails
Combining like terms:
E(X) = 0.2 * Number of Tails + 0.4 * 320
Now, let's solve for Number of Tails by setting E(X) equal to the value we're trying to find (the expected number of tails):
0.2 * Number of Tails + 0.4 * 320 = Expected Number of Tails
The expected number of tails when flipping the coin 320 times can be found by solving this equation.