Get reliable answers to your questions at Westonci.ca, where our knowledgeable community is always ready to help. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
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].
### 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].
Thank you for visiting our platform. We hope you found the answers you were looking for. Come back anytime you need more information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.
