Answered

Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

Jane has 21 biscuits in a tin:
- 9 plain biscuits
- 7 chocolate biscuits
- 5 currant biscuits

Jane takes two biscuits at random from the tin. Work out the probability that the two biscuits are not of the same type.

Sagot :

GinnyAnswer
Sure, let's solve this problem step-by-step.

### Step 1: Determine the total number of biscuits and their types.
- Total number of biscuits: 21
- Plain biscuits: 9
- Chocolate biscuits: 7
- Currant biscuits: 5

### Step 2: Calculate the probability that both biscuits are the same type.

#### Probability of drawing two plain biscuits:
- Probability of the first biscuit being plain: [tex]\(\frac{9}{21}\)[/tex]
- Probability of the second biscuit being plain (once one plain biscuit is already taken): [tex]\(\frac{8}{20}\)[/tex]

So, the probability of both being plain is:
[tex]\[ \frac{9}{21} \times \frac{8}{20} = \frac{72}{420} = \frac{36}{210} \approx 0.17142857142857143 \][/tex]

#### Probability of drawing two chocolate biscuits:
- Probability of the first biscuit being chocolate: [tex]\(\frac{7}{21}\)[/tex]
- Probability of the second biscuit being chocolate (once one chocolate biscuit is already taken): [tex]\(\frac{6}{20}\)[/tex]

So, the probability of both being chocolate is:
[tex]\[ \frac{7}{21} \times \frac{6}{20} = \frac{42}{420} = \frac{21}{210} \approx 0.09999999999999999 \][/tex]

#### Probability of drawing two currant biscuits:
- Probability of the first biscuit being currant: [tex]\(\frac{5}{21}\)[/tex]
- Probability of the second biscuit being currant (once one currant biscuit is already taken): [tex]\(\frac{4}{20}\)[/tex]

So, the probability of both being currant is:
[tex]\[ \frac{5}{21} \times \frac{4}{20} = \frac{20}{420} = \frac{10}{210} \approx 0.047619047619047616 \][/tex]

### Step 3: Calculate the total probability of both biscuits being the same type.
We sum up the probabilities of each case:
[tex]\[ 0.17142857142857143 + 0.09999999999999999 + 0.047619047619047616 = 0.31904761904761905 \][/tex]

### Step 4: Calculate the probability that the two biscuits are not the same type.

The probability of the two biscuits being not the same type is given by:
[tex]\[ 1 - \text{(probability that both are the same)} = 1 - 0.31904761904761905 \approx 0.680952380952381 \][/tex]

### Conclusion
The probability that Jane takes two biscuits of not the same type is approximately [tex]\(0.680952380952381\)[/tex].
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.