I'm so lost with this stuff!
2.
What is the P (A) if we know that the odds in favor of A occurring are 3 to 4? (See section 9.4)
3.
Find the P (not A) in the situation presented in question 2 above.
4.
The lottery payoff in a letter game at a church social is determined by the single letter the winner holds. There are four letters, A, B, C, and D. The probabilities that each will be drawn are 1243,,, and 10101010
, respectively. The payoffs are $2 for an A, $4 for a B, $8 for a C, and $10 for a D. Compute the expected value of the game. (see page 528)
5.
If 3()5PA=, what are the odds in favor of A occurring?
<<The probabilities that each will be drawn are 1243,,, and 10101010
, respectively.>>
You can't be serious. How are we supposed to make sense out of that?
2. To find the probability of event A, given the odds in favor of A occurring, you can use the odds formula. The odds are given in the form of "3 to 4," which means the ratio of favorable outcomes to unfavorable outcomes is 3:4.
To calculate the probability, first add the numbers in the ratio to get the total number of equal parts: 3 + 4 = 7. Then, divide the number of favorable outcomes (3) by the total number of equal parts (7).
So, the probability of event A occurring is 3/7.
3. To find the probability of not event A (P(not A)), subtract the probability of event A (P(A)) from 1. In question 2, we found P(A) to be 3/7.
Therefore, P(not A) = 1 - P(A) = 1 - 3/7 = 4/7.
4. To compute the expected value of the game, you need to multiply the value associated with each outcome by its probability and then sum them up.
The probabilities for each letter are given as 1/2, 1/4, 1/8, and 1/10, respectively, totaling 1 (or 100% probability).
The expected value can be calculated using the formula:
Expected Value = (Probability of A * Value of A) + (Probability of B * Value of B) + (Probability of C * Value of C) + (Probability of D * Value of D)
In this case, the expected value would be:
(1/2 * $2) + (1/4 * $4) + (1/8 * $8) + (1/10 * $10) = $1 + $1 + $1 + $1 = $4.
So, the expected value of the game is $4.
5. The given expression '3()5PA=' appears to be incomplete or incorrect. Please provide the complete and correct expression for further analysis.