Harry Potter is at Ollivanders Wand Shop. As we all know, the wand must choose the wizard, so Harry cannot make the choice himself. He interprets the wand selection as a random process so he can determine the probabilities of different outcomes.
The wood types available are holly, elm, maple, and wenge. The core materials on offer are phoenix feather, unicorn hair, dragon scale, raven feather, and thestral tail.
Let A be the event that Harry is chosen by a wand made of holly and B be the event that he is chosen by a wand with a dragon scale core.

The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%

Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).

In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;

P(A) = Number of required outcomes/Number of all possible outcomes

P(A) = 1/4 or (0.25)

To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;

P(B) = Number of required outcomes/Number of all possible outcomes

P(B) = 1/5 or (0.20)

However, the question requires the probability of P(A or B).

First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;

P(A and B) = P(A) x P(B)

P(A and ) = 1/4 x 1/5

P(A and B) = 1/20 (0.05)

The probability of P(A or B) can now be calculated as follows;

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = (0.25 +0.20) - 0.05

P(A or B) = 0.45 - 0.05

P(A or B) = 0.40

Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%