Probability Textbook Exercise - Corbettmaths - Free Printable

Problem Analysis and Solution

The image contains two probability questions. Let's solve each question step by step.

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#### Question 1:
Theo has 3 red sweets and 2 white sweets. He picks a sweet at random.

##### (a) Write down the probability that Theo picks a red sweet.
- Total number of sweets: \( 3 \text{ (red)} + 2 \text{ (white)} = 5 \)
- Number of red sweets: \( 3 \)
- Probability of picking a red sweet:
\[
P(\text{Red}) = \frac{\text{Number of red sweets}}{\text{Total number of sweets}} = \frac{3}{5}
\]

##### (b) Write down the probability that Theo picks a white sweet.
- Number of white sweets: \( 2 \)
- Probability of picking a white sweet:
\[
P(\text{White}) = \frac{\text{Number of white sweets}}{\text{Total number of sweets}} = \frac{2}{5}
\]

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#### Question 2:
Leah has 12 cards, each with a shape on it. She takes a card at random.

From the image, the shapes on the cards are as follows:
- Star: 1 card
- Triangle: 5 cards
- Circle: 6 cards

##### (a) What is the probability that Leah takes a card with a star on it?
- Total number of cards: \( 12 \)
- Number of cards with a star: \( 1 \)
- Probability of picking a card with a star:
\[
P(\text{Star}) = \frac{\text{Number of cards with a star}}{\text{Total number of cards}} = \frac{1}{12}
\]

##### (b) What is the probability that Leah takes a card with a triangle on it?
- Number of cards with a triangle: \( 5 \)
- Probability of picking a card with a triangle:
\[
P(\text{Triangle}) = \frac{\text{Number of cards with a triangle}}{\text{Total number of cards}} = \frac{5}{12}
\]

##### (c) What is the probability that Leah takes a card with a circle on it?
- Number of cards with a circle: \( 6 \)
- Probability of picking a card with a circle:
\[
P(\text{Circle}) = \frac{\text{Number of cards with a circle}}{\text{Total number of cards}} = \frac{6}{12} = \frac{1}{2}
\]

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Final Answers:

1. (a) \( \boxed{\frac{3}{5}} \)
(b) \( \boxed{\frac{2}{5}} \)

2. (a) \( \boxed{\frac{1}{12}} \)
(b) \( \boxed{\frac{5}{12}} \)
(c) \( \boxed{\frac{1}{2}} \)