Each round of the game costs $1 to play. A round consists of you choosing a number from 1 to 10 and then picking a card at random from a standard deck of cards. I fyou pick a card with the number you chose, you win $5. If you don't, you lose your dollar.
a) What is the probability that you can win? What is the probability you can lose?
Using a standar deck of 52 cards, what is the probability of drawing four cards of the same number(eg.four aces, 4 kings, fiyr 2s, four 3s,etc?
The probability of winning is obviously 1/10 and the probability of losing is 1 minus that (9/10). Those are not the important numbers. What matters is the expected gain or loss, taking the amount of the "pot" into account..
There is a 1/10 chance of winning $5 (and your dollar back, presumably). That is an average return of 0.60, but there is a $1 cost to play each time, so on the average 40 cents is lost each time.
The expected return is a 40 cent loss per round. Those are pretty bad odds for the bettor.
To calculate the probability of winning or losing, we need to determine the number of favorable outcomes and the total number of possible outcomes.
In this case, the favorable outcome is drawing a card with a number that matches the number chosen. Since there are 10 numbers to choose from, each with one favorable outcome, the number of favorable outcomes is 10.
The total number of possible outcomes is the total number of cards in a standard deck, which is 52.
So, the probability of winning can be calculated as the ratio of favorable outcomes to total outcomes:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
= 10 / 52
= 5 / 26
Therefore, the probability of winning is 5/26.
To find the probability of losing, we can subtract the probability of winning from 1, since the sum of the probabilities of all possible outcomes must equal 1:
Probability of losing = 1 - Probability of winning
= 1 - (5/26)
= 21/26
Hence, the probability of losing is 21/26.