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Question 1196639: A relief organization must track their supply and demand for various blood types. They estimate that about 46% of the population in a country has Type O blood, 42% Type A, 9% Type B, and the rest Type AB.
a) If someone volunteers to give blood, what is the probability that this donor: i) Has Type AB blood? ii) Has Type A or Type B blood? iii) Is not Type O?
b) Among four potential donors, what is the probability that: i) All are Type O? ii) None have Type AB blood? iii) Not all are Type A? iv) At least one person is Type B?
Answer by ElectricPavlov(122)   (Show Source):
You can put this solution on YOUR website! **a) Probabilities for a Single Donor**
* **i) Has Type AB blood:**
* Probability = 100% - (46% + 42% + 9%) = 3%
* **ii) Has Type A or Type B blood:**
* Probability = 42% + 9% = 51%
* **iii) Is not Type O blood:**
* Probability = 100% - 46% = 54%
**b) Probabilities for Four Donors**
* **i) All are Type O:**
* Probability = (0.46) * (0.46) * (0.46) * (0.46) = 0.46^4 ≈ 0.0457 (or 4.57%)
* **ii) None have Type AB blood:**
* Probability of not having Type AB = 100% - 3% = 97%
* Probability that none have Type AB = (0.97) * (0.97) * (0.97) * (0.97) = 0.97^4 ≈ 0.8853 (or 88.53%)
* **iii) Not all are Type A:**
* Probability that all are Type A = (0.42) * (0.42) * (0.42) * (0.42) = 0.42^4 ≈ 0.0311 (or 3.11%)
* Probability that not all are Type A = 100% - 3.11% = 96.89%
* **iv) At least one person is Type B:**
* Probability that none are Type B = (1 - 0.09)^4 = 0.6860
* Probability that at least one person is Type B = 100% - 68.60% = 31.40%
**Note:** These calculations assume that the blood types of the donors are independent of each other.
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