Harry Potter in Gryffindor?

According to the question, the sorting hat's decision was random, so the probability that Harry is placed in Gryffindor is $\dfrac14$

But, as Harry chose Gryffindor as his preference, so the probability of him being in Gryffindor increased by $\dfrac14 \times \dfrac{50}{100} = \dfrac18$

Hence, probability that Harry is in Gryffindor, considering all the cases is: $\dfrac14+\dfrac18=\dfrac38 = 0.375$

Finally, the answer is $1000\times 0.375=\boxed{375}$

The original probability that a student gets sorted in a house is 1/4. But since Harry prefers to be sorted in Gryffindor, that probability increased by 50%. So 1/4 + ((1/4) * (1/2)) = 3/8. 3/8 * 1000 = 375

Initial Probability = 1/4 When Harry chose Griffindor Probability = 1/4 * (100+50)/100
'.' P= 3/8 1000P = 375

The key thing to note is that Griffyndor's probability is raised by 50% of itself . Let's say the final probability of going to Griffyndor is G . Let's also say the original probability of going there is g

The correct equation: G = g + (1/2) * g

Incorrect equation: G = g + 0.5

Just plug in 1/4 for g and you're golden!

It's a good thing we had 3 tries for this one, or I would have messed it up!

50% of 25% = %12.5

25% + 12.5% = 100P

37.5 * 10 = 1000P = 375

The initial probability of getting chosen to Gryffindor was $\frac 14$ . But it is said that the probability would increase by $\frac 12$ from the initial $\frac 14$ means the new probability would be $\frac 14 \times \frac 32$ $1000 \times \frac 38 = 375$