Answer: 97
Step-by-step explanation: The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 (sequence) just if you need all the primes
Aaaaaaaaaaaaaaaaaaaaaaaaaaaaa I’m not sure about this yet so I’m sorry bye
Answer:
The probability that the coin landed heads is 65.3%.
Step-by-step explanation:
Given : Urn A has 5 white and 17 red balls. Urn B has 9 white and 12 red balls. We flip a fair coin. If the outcome is heads, then a ball from urn A is selected, whereas if the outcome is tails, then a ball from urn B is selected. Suppose that a white ball is selected.
To find : What is the probability that the coin landed heads ?
Solution :
Let the event A be the ball taken from Urn A (5 white and 17 red balls)
Let B=A'- the ball taken from urn B(9 white and 12 red balls)
Let W be event that a white ball is selected.
An urn is chosen based on a toss of a fair coin.
P(A) = coin landed on heads = ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
P(B) = coin landed on tails = ![P(A')=\frac{1}{2}](https://tex.z-dn.net/?f=P%28A%27%29%3D%5Cfrac%7B1%7D%7B2%7D)
and ![P(W/B)=\frac{3}{7}](https://tex.z-dn.net/?f=P%28W%2FB%29%3D%5Cfrac%7B3%7D%7B7%7D)
Using Bayes formula,
![P(B/W)=\dfrac{P(W/B)P(B)}{P(W/B)P(B)+P(W/A)P(A)}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7BP%28W%2FB%29P%28B%29%7D%7BP%28W%2FB%29P%28B%29%2BP%28W%2FA%29P%28A%29%7D)
![P(B/W)=\dfrac{\frac{3}{7}\times \frac{1}{2}}{\frac{3}{7}\times \frac{1}{2}+\frac{5}{22}\times \frac{1}{2}}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B%5Cfrac%7B3%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%7D%7B%5Cfrac%7B3%7D%7B7%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%2B%5Cfrac%7B5%7D%7B22%7D%5Ctimes%20%5Cfrac%7B1%7D%7B2%7D%7D)
![P(B/W)=\dfrac{\frac{3}{14}}{\frac{3}{14}+\frac{5}{44}}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B%5Cfrac%7B3%7D%7B14%7D%7D%7B%5Cfrac%7B3%7D%7B14%7D%2B%5Cfrac%7B5%7D%7B44%7D%7D)
![P(B/W)=\dfrac{\frac{3}{14}}{\frac{132+70}{14\times 44}}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B%5Cfrac%7B3%7D%7B14%7D%7D%7B%5Cfrac%7B132%2B70%7D%7B14%5Ctimes%2044%7D%7D)
![P(B/W)=\dfrac{\frac{3}{14}}{\frac{202}{616}}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B%5Cfrac%7B3%7D%7B14%7D%7D%7B%5Cfrac%7B202%7D%7B616%7D%7D)
![P(B/W)=\dfrac{3\times 616}{14\times 202}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B3%5Ctimes%20616%7D%7B14%5Ctimes%20202%7D)
![P(B/W)=\dfrac{66}{101}](https://tex.z-dn.net/?f=P%28B%2FW%29%3D%5Cdfrac%7B66%7D%7B101%7D)
![P(B/W)=65.3\%](https://tex.z-dn.net/?f=P%28B%2FW%29%3D65.3%5C%25)
Therefore, the probability that the coin landed heads is 65.3%.
Answer:
252 inches squared is the answer
Step-by-step explanation: