A new bag of golf tees contains 10 red tees, 10 orange tees, 10 hreen tees and 10 blue tees. You empty the tees into your golf bag. What is the probability of grabbing out two tees of the same color in a row for you and your partner?
To find the probability of grabbing out two tees of the same color in a row for you and your partner, we need to consider the total number of possible outcomes and the favorable outcomes.
Total number of possible outcomes:
When you and your partner are picking two tees out of the bag, there are a total of 40 tees to choose from initially.
Favorable outcomes:
To calculate the favorable outcomes, we need to consider each color separately.
Red tees:
Initially, there are 10 red tees in the bag.
For you to pick a red tee, there are 10 red tees out of 40 total tees. So the probability of you picking a red tee is 10/40.
After you pick a red tee, there are 9 red tees left out of the total of 39 tees. So the probability of your partner picking a red tee is 9/39.
Therefore, the probability of grabbing two red tees in a row is (10/40) * (9/39).
Following the same logic, the probability of grabbing two tees of the same color for each of the other colors can be determined:
Orange tees: (10/40) * (9/39)
Green tees: (10/40) * (9/39)
Blue tees: (10/40) * (9/39)
Now, since we want the probability of grabbing two tees of the same color for any color, we need to add up the probabilities for each color since they are mutually exclusive events:
P(grabbing two tees of the same color) = P(grabbing two red tees) + P(grabbing two orange tees) + P(grabbing two green tees) + P(grabbing two blue tees)
P(grabbing two tees of the same color) = [(10/40) * (9/39)] + [(10/40) * (9/39)] + [(10/40) * (9/39)] + [(10/40) * (9/39)]
By simplifying this expression, we can find the final probability.