Question

a bag contains 9 red marbles, 7 white marbles, and 7 blue marbles. you draw 3 marbles out at random, without replacement. find the following probabilities and round to 4 decimal places. a. the probability that all the marbles are red is enter an integer or decimal number, accurate to at least 4 decimal places more.. b. the probability that none of the marbles are red is

Explanation:

Step1: Total marbles

Total = 9 + 7 + 7 = 23

Step2: Total ways to draw 3 marbles

$C(23,3) = \frac{23×22×21}{3×2×1} = 1771$

Step3: Favorable for all red

$C(9,3) = \frac{9×8×7}{3×2×1} = 84$

Step4: Probability a

$\frac{84}{1771} ≈ 0.0474$

Step5: Non-red marbles

Non-red = 7 + 7 = 14

Step6: Favorable for none red

$C(14,3) = \frac{14×13×12}{3×2×1} = 364$

Step7: Probability b

$\frac{364}{1771} ≈ 0.2055$

Answer:

a. 0.0474
b. 0.2055