Question 1168481
Let's solve this problem using Bayes' Theorem.

**1. Define Events**

* **H:** Coin lands heads.
* **T:** Coin lands tails.
* **W:** A white ball is selected.

**2. Given Probabilities**

* P(H) = 1/2 (fair coin)
* P(T) = 1/2 (fair coin)
* P(W | H) = 2/15 (probability of white ball from urn A)
* P(W | T) = 14/20 = 7/10 (probability of white ball from urn B)

**3. Bayes' Theorem**

We want to find P(H | W), the probability that the coin landed heads given that a white ball was selected.

Bayes' Theorem states:

P(H | W) = [P(W | H) * P(H)] / P(W)

**4. Calculate P(W)**

We need to calculate P(W), the probability of selecting a white ball. We can use the law of total probability:

P(W) = P(W | H) * P(H) + P(W | T) * P(T)

P(W) = (2/15) * (1/2) + (7/10) * (1/2)

P(W) = 1/15 + 7/20

P(W) = (4 + 21) / 60

P(W) = 25/60 = 5/12

**5. Calculate P(H | W)**

Now, we can use Bayes' Theorem:

P(H | W) = [P(W | H) * P(H)] / P(W)

P(H | W) = [(2/15) * (1/2)] / (5/12)

P(H | W) = (1/15) / (5/12)

P(H | W) = (1/15) * (12/5)

P(H | W) = 12/75 = 4/25

**6. Final Answer**

The probability that the coin landed heads given that a white ball was selected is 4/25.