A box contains 2 green balls and 3 blue balls. A ball is selected at random from the box and not replaced. A second ball is then selected. What is the probability of selecting two balls of different colours?

Question

Asked on July 13, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-07-13T06:53:30.710Z

Here's how to solve this probability problem: Step 1: Determine the initial probabilities. There are 2 green balls (G) and 3 blue balls (B), making a total of 2+3=5 balls. The probability of selecting a green ball first is P(G_1) = (2)/(5). The probability of selecting a blue ball first is P(B_1) = (3)/(5). Step 2: Draw a tree diagram to illustrate the outcomes. Since the first ball is not replaced, there will be 4 balls remaining for the second selection. First Selection: Branch 1: Green (G) Probability: P(G_1) = (2)/(5) Remaining balls: 1 Green, 3 Blue (Total 4) Second Selection (after G1): Sub-branch 1.1: Green (G) Probability: P(G_2 | G_1) = (1)/(4) Combined outcome: GG Combined probability: P(G_1 and G_2) = (2)/(5) × (1)/(4) = (2)/(20) Sub-branch 1.2: Blue (B) Probability: P(B_2 | G_1) = (3)/(4) Combined outcome: GB Combined probability: P(G_1 and B_2) = (2)/(5) × (3)/(4) = (6)/(20) Branch 2: Blue (B) Probability: P(B_1) = (3)/(5) Remaining balls: 2 Green, 2 Blue (Total 4) Second Selection (after B1): Sub-branch 2.1: Green (G) Probability: P(G_2 | B_1) = (2)/(4) = (1)/(2) Combined outcome: BG Combined probability: P(B_1 and G_2) = (3)/(5) × (2)/(4) = (6)/(20) Sub-branch 2.2: Blue (B) Probability: P(B_2 | B_1) = (2)/(4) = (1)/(2) Combined outcome: BB Combined probability: P(B_1 and B_2) = (3)/(5) × (2)/(4) = (6)/(20) Step 3: Identify the outcomes for selecting two balls of different colours. The outcomes where two balls of different colours are selected are: • Green then Blue (GB) • Blue then Green (BG) Step 4: Calculate the total probability for selecting two balls of different colours. We sum the probabilities of the identified outcomes: P(different colours) = P(G_1 and B_2) + P(B_1 and G_2) P(different colours) = (6)/(20) + (6)/(20) P(different colours) = (12)/(20) P(different colours) = (3)/(5) The probability of selecting two balls of different colours is (3)/(5). Send me the next one 📸

Accepted Answer · 2026-07-13T06:53:30.710Z

Here's how to solve this probability problem: Step 1: Determine the initial probabilities. There are 2 green balls (G) and 3 blue balls (B), making a total of 2+3=5 balls. The probability of selecting a green ball first is P(G_1) = (2)/(5). The probability of selecting a blue ball first is P(B_1) = (3)/(5). Step 2: Draw a tree diagram to illustrate the outcomes. Since the first ball is not replaced, there will be 4 balls remaining for the second selection. First Selection: Branch 1: Green (G) Probability: P(G_1) = (2)/(5) Remaining balls: 1 Green, 3 Blue (Total 4) Second Selection (after G1): Sub-branch 1.1: Green (G) Probability: P(G_2 | G_1) = (1)/(4) Combined outcome: GG Combined probability: P(G_1 and G_2) = (2)/(5) × (1)/(4) = (2)/(20) Sub-branch 1.2: Blue (B) Probability: P(B_2 | G_1) = (3)/(4) Combined outcome: GB Combined probability: P(G_1 and B_2) = (2)/(5) × (3)/(4) = (6)/(20) Branch 2: Blue (B) Probability: P(B_1) = (3)/(5) Remaining balls: 2 Green, 2 Blue (Total 4) Second Selection (after B1): Sub-branch 2.1: Green (G) Probability: P(G_2 | B_1) = (2)/(4) = (1)/(2) Combined outcome: BG Combined probability: P(B_1 and G_2) = (3)/(5) × (2)/(4) = (6)/(20) Sub-branch 2.2: Blue (B) Probability: P(B_2 | B_1) = (2)/(4) = (1)/(2) Combined outcome: BB Combined probability: P(B_1 and B_2) = (3)/(5) × (2)/(4) = (6)/(20) Step 3: Identify the outcomes for selecting two balls of different colours. The outcomes where two balls of different colours are selected are: • Green then Blue (GB) • Blue then Green (BG) Step 4: Calculate the total probability for selecting two balls of different colours. We sum the probabilities of the identified outcomes: P(different colours) = P(G_1 and B_2) + P(B_1 and G_2) P(different colours) = (6)/(20) + (6)/(20) P(different colours) = (12)/(20) P(different colours) = (3)/(5) The probability of selecting two balls of different colours is (3)/(5). Send me the next one 📸

A box contains 2 green balls and 3 blue balls. A ball is selected at random from the box and not replaced. A second ball is then selected. What is the probability of selecting two balls of different colours?

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A box contains 2 green balls and 3 blue balls. A ball is selected at random from the box and not replaced. A second ball is then selected. What is the probability of selecting two balls of different colours?

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