37. A box whole, twored balls, if two balls are selected at random find the probability that
a) one red and one white ball are selected
b) two of the same color is selected
c) no white balls are selected
d) no read balls are selected
To calculate the probabilities, we first need to determine the total number of possible outcomes and the number of favorable outcomes for each situation.
Given:
- Total number of balls in the box = 37
- Number of red balls = 2
- Number of white balls = 35
a) Probability of selecting one red and one white ball:
To find this probability, we need to consider the number of ways we can choose one red ball and one white ball out of the total number of balls.
Total number of ways to choose one red ball out of two: C(2, 1) = 2
Total number of ways to choose one white ball out of 35: C(35, 1) = 35
Total number of ways to choose two balls out of 37: C(37, 2) = (37 * 36) / (2 * 1) = 666
Favorable outcomes (one red and one white): 2 * 35 = 70
Probability of selecting one red and one white ball: Favorable outcomes / Total outcomes = 70/666 ≈ 0.105 (rounded to three decimal places)
b) Probability of selecting two balls of the same color:
To find this probability, we need to consider the number of ways we can choose two red balls or two white balls from the total number of balls.
Total number of ways to choose two red balls out of two: C(2, 2) = 1
Total number of ways to choose two white balls out of 35: C(35, 2) = (35 * 34) / (2 * 1) = 595
Favorable outcomes (two balls of the same color): 1 + 595 = 596
Probability of selecting two balls of the same color: Favorable outcomes / Total outcomes = 596/666 ≈ 0.895 (rounded to three decimal places)
c) Probability of selecting no white balls:
To find this probability, we need to consider the number of ways we can choose two red balls from the total number of balls.
Total number of ways to choose two red balls out of two: C(2, 2) = 1
Favorable outcomes (no white balls): 1
Probability of selecting no white balls: Favorable outcomes / Total outcomes = 1/666 ≈ 0.002 (rounded to three decimal places)
d) Probability of selecting no red balls:
To find this probability, we need to consider the number of ways we can choose two white balls from the total number of balls.
Total number of ways to choose two white balls out of 35: C(35, 2) = (35 * 34) / (2 * 1) = 595
Favorable outcomes (no red balls): 595
Probability of selecting no red balls: Favorable outcomes / Total outcomes = 595/666 ≈ 0.893 (rounded to three decimal places)