Question

An evil sorcerer forces harry potter to drink 7 randomly selected potions from a basket of 20 potions, 4 of which are cursed.

1. What is the probability that none of the potions harry drinks are cursed

2. Harry’s wand breaks as soon as he has drinken 4 cursed potions. Let X be the number of cursed potions harry drinks. (X cannot be greater than 4, even if he drank more 4 cursed potions.)

If f(x) is the p.m.f of X, what is f(3)

Answer 1

The probability that none of the 7 selected potions harry drinks are cursed is computed here as:

= Number of ways to select 7 potions from 16 non cursed potions / Total ways to select 7 potions from 20 potions

Therefore 0.1476 is the required probability here.

Now the general probability function for X that is the number of cursed potions in the 7 selected potions is computed here as:

P(X = x) = Number of ways to select x cursed potions from 4 cursed potions * Number of ways to select (7 - x) non cursed potions from 16 non cursed potions / Total ways to select 7 potions from 20 potions

This is the required PMF for X here.

The probability thus is computed here as:

Therefore 0.0939 is the required probability here.