Mark wants a new car that costs $30000. He only has $500 in his savings account and $300 in his checking account. Which financin
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Probabilities are used to determine the chances of Laura winning an activity
- The value of p is 1/12
- The expected score of the game is -1/6
- The probability that she has a total score of 5 after two rounds is 0
To calculate the value of p, we make use of the following probability formula
So, we have:
Collect like terms
Evaluate the sums, on the left-hand side
Subtract 11/12 from both sides
Hence, the value of p is 1/12
<h3>(b) How to calculate the expected score</h3>This is calculated using the following expected value formula
So, we have:
Evaluate the products
Simplify
Hence, the expected score of the game is -1/6
<h3>(c) The probability that she has a total score of 5 after two rounds</h3>From the table, we have:
For after two rounds, we make use of the following equation
Hence, the probability that she has a total score of 5 after two rounds is 0
Read more about probabilities at:
This is not an identity but an equation. You're supposed to find the values of for which this is true. It is *not* true for all values of
.
To see why:
has period
, which means
.
The angle sum identity for says that
So
By definition of ,
and so
which is only 0 if either (which only happens for certain values of
) or
(which also only happens for certain values of
). It's these values of
you want to find.
whenever
is a multiple of
, i.e.
for any integer
.
If , then
is true for
and
. Then to account for all other possible values, we add a multiple of
, so that
or
for integers
.