Mathematics: 1. a bag has 5 red marbles, 6 blue marbles and 4 black marbles. what is the probability of picking a red marble, replacing it, and then picking another red marble? 2. a bag has 5 red marbles, 6 blue marbles and 4 black marbles. what is the probability of picking a blue marble, replacing it, and then picking a black marble? 3. a bag contains 4 white marbles, 3 black marbles, and 5 red marbles. find the probability of picking a red marble? 4. a bag contains 3 white marbles, 2 black marbles, and 5

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1. a bag has 5 red marbles, 6 blue marbles and

CassidgTab

12.01.2022

(1) $\frac{1}{9}$

(2) $\frac{8}{75}$

(3) $\frac{5}{12}$

(4) $\frac{3}{10}$

Step-by-step explanation:

(1). A bag has 5 red marbles, 6 blue marbles and 4 black marbles.

Total marbles in a bag = 5 + 6 + 4 = 15 marbles

The probability of picking a red marble $P_{1}$ = $\frac{5}{15}$ = $\frac{1}{3}$

By replacing it and then picking another red marble $P_{2}$ = $\frac{5}{15}$ = $\frac{1}{3}$

P = $\frac{1}{3}$ × $\frac{1}{3}$ = $\frac{1}{9}$

(2). A bag has 5 red marbles, 6 blue marbles and 4 black marbles.

Total marbles in a bag = 5 + 6 + 4 = 15 marbles.

The probability of picking a blue marble = $P_{1}$ = $\frac{6}{15}$ = $\frac{2}{5}$

replacing it and then picking a black marble = $P_{2}$ = $\frac{4}{15}$

P = $\frac{2}{5}$ × $\frac{4}{15}$ = $\frac{8}{75}$

(3). A bag contains 4 white, 3 black and 5 red marbles.

Total marbles = 4 + 3 + 5 = 12 marbles

The probability of picking a red marble = $\frac{5}{12}$

(4). A bag contains 3 white marbles, 2 black marbles and 5 red marbles.

Total marbles = 3 + 2 + 5 = 10 marbles.

The probability of picking a white marble = $\frac{3}{10}$

(1) $\frac{1}{9}$

(2) $\frac{8}{75}$

(3) $\frac{5}{12}$

(4) $\frac{3}{10}$

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