In a carnival fishing game, the player is given a net to catch plastic fish. The player is allowed to scoop up 4 fish from a pool containing 36 fish, one of which is the winning fish. What is the probability of winning the game?
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I am having a hard time with probability and struggling with what steps to do.
probability of winning = 1 - probability of losing
none on first scoop = 35/36
now you have 35 in there
none on second scoop = 34/35
none on third scoop = 33/34
none on fourth scoop = 32/33
so probability of getting NONE in 4 scoops
= 35/36 * 34/35 * 33/34 * 32/33
so
1 - that
Oh, so this is a dependent event. Thank you! :)
To determine the probability of winning the game, we first need to calculate the total number of possible outcomes, and then determine the number of favorable outcomes.
Step 1: Calculate the total number of possible outcomes.
In this case, the total number of possible outcomes is the number of ways to choose 4 fish from a pool of 36 fish, without any specific order being required. This can be calculated using the combination formula nCr, where n is the total number of fish in the pool and r is the number of fish the player is allowed to catch. So, in this case, it is calculated as:
Total number of possible outcomes = 36C4 = (36!)/(4!(36-4)!) = 36!/(4!32!) = (36*35*34*33)/(4*3*2*1) = 58905
Step 2: Determine the number of favorable outcomes.
Since we are only interested in the player catching the winning fish, there is only 1 favorable outcome, which is catching the winning fish itself.
Step 3: Calculate the probability of winning the game.
The probability of winning the game is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability of winning the game = (Number of favorable outcomes)/(Total number of possible outcomes) = 1/58905 ≈ 0.000017%
Therefore, the probability of winning the game is approximately 0.000017%.
To calculate the probability of winning the game, we first need to determine the total number of possible outcomes and the number of favorable outcomes.
In this scenario, there are 36 fish in the pool, and the player is allowed to scoop up 4 fish. Therefore, the total number of possible outcomes is the number of ways to choose 4 fish out of 36, which can be calculated using combinations.
The formula for combinations is:
nCr = n! / ((n-r)! * r!)
Where n is the total number of items and r is the number of items chosen.
Let's calculate the total number of possible outcomes:
36C4 = 36! / ((36-4)! * 4!) = (36 * 35 * 34 * 33) / (4 * 3 * 2 * 1) = 58905
So there are 58905 possible outcomes in this game.
Now let's determine the number of favorable outcomes, which is the number of ways to choose the winning fish among the 4 fish caught. Since there is only 1 winning fish in the pool, and the player is allowed to catch 4 fish, there are 4 ways to choose the winning fish.
Therefore, the number of favorable outcomes is 4.
Now, we can calculate the probability of winning the game by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes = 4 / 58905
So, the probability of winning the game is approximately 0.000068 or 0.0068%.