20. A bag contains 7 red chips and 10 blue chips. Two chips are selected randomly without replacement from the bag. What is the probability that both chips are red
To find the probability of selecting two red chips, we first need to calculate the total number of ways to select two chips from the bag without replacement.
The total number of chips in the bag is 7 (red) + 10 (blue) = 17 chips.
So, the total number of ways to select two chips from the bag is given by the combination equation: C(17, 2).
C(17, 2) = 17! / (2! * (17-2)!), where "!" denotes the factorial of a number.
Simplifying this expression, we have:
C(17, 2) = 17! / (2! * 15!)
= (17 * 16 * 15!) / (2! * 15!)
= (17 * 16) / 2
= 136
Therefore, there are 136 different ways to select two chips from the bag without replacement.
Next, let's calculate the number of ways to select two red chips from the bag.
Since there are 7 red chips in the bag, we use the combination equation: C(7, 2).
C(7, 2) = 7! / (2! * (7-2)!)
= (7 * 6 * 5!) / (2! * 5!)
= (7 * 6) / 2
= 21
So, there are 21 different ways to select two red chips from the bag.
Finally, the probability of selecting two red chips is given by the number of ways to select two red chips divided by the total number of ways to select two chips:
Probability = Number of ways to select two red chips / Total number of ways to select two chips
= 21 / 136
≈ 0.1544 or 15.44% (rounded to four decimal places)
Therefore, the probability of selecting both chips as red is approximately 0.1544, or 15.44%.