Class 9 - Chapter 7: The mathematics of maybe: Introduction to Probability

Given:

• Basket A: 1 Apple (A), 2 Oranges (O)
• Basket B: 1 Banana (B), 1 Mango (M)

(i) Tree Diagram

Basket A
│
├── Apple
│    ├── Banana  → (Apple, Banana)
│    └── Mango   → (Apple, Mango)
│
├── Orange
│    ├── Banana  → (Orange, Banana)
│    └── Mango   → (Orange, Mango)
│
└── Orange
     ├── Banana  → (Orange, Banana)
     └── Mango   → (Orange, Mango)

(ii) Sample Space

S = { (Apple, Banana), (Apple, Mango), (Orange, Banana), (Orange, Mango), (Orange, Banana), (Orange, Mango) }

Total possible outcomes = 6

(iii) Probability of Picking One Apple and One Banana

Favourable outcome:

(Apple, Banana)

Number of favourable outcomes = 1

Total outcomes = 6

P(Apple and Banana) = 1/6

Answer: 1/6

Given:

• 3 Red pens
• 4 Black pens
• 2 Green pens

Total pens = 9

Pen is replaced after the first pick.

(i) Possible Outcomes

Let:

• R = Red
• B = Black
• G = Green

Sample Space:

S = { (R,R), (R,B), (R,G), (B,R), (B,B), (B,G), (G,R), (G,B), (G,G) }

Tree Diagram

You
│
├── Red
│    ├── Red    → (R,R)
│    ├── Black  → (R,B)
│    └── Green  → (R,G)
│
├── Black
│    ├── Red    → (B,R)
│    ├── Black  → (B,B)
│    └── Green  → (B,G)
│
└── Green
     ├── Red    → (G,R)
     ├── Black  → (G,B)
     └── Green  → (G,G)

(ii) Probability That Both Pick Pens of the Same Colour

Since replacement is done:

P(Red) = 3/9 = 1/3

P(Black) = 4/9

P(Green) = 2/9

Probability both pick Red:

(1/3)(1/3) = 1/9

Probability both pick Black:

(4/9)(4/9) = 16/81

Probability both pick Green:

(2/9)(2/9) = 4/81

Total probability:

1/9 + 16/81 + 4/81

= 9/81 + 16/81 + 4/81

= 29/81

Answer:

P(Same Colour) = 29/81

≈ 0.358

≈ 35.8%