Question

1.    One of the letters in WIN appears under each bottle cap for Sparky Juice. To win a prize, you must collect all three letters. You are equally likely to get any of the three letters with each bottle. What is the probability that you will win after buying exactly three bottles?

2.    A license plate contains three numerals. Even and odd digits are equally likely. What is the probability that all three numerals are even?

3.    A restaurant gives away a model car with each meal. You are equally likely to get any of the five cars. What is the probability that you will get two of the same car after two meals?

Answer 1

Question 1

One of the letters in WIN appears under each bottle cap for sparky juice.

To win a prize, I must collect all 3 letters.

We are equally likely to get any of the 3 letters with each bottle. So, the chance of getting a W, a I, or a N, is all 1/3.

We have to find the probability that I will win the prize, exactly after buying 3 bottles.

Now, in these 3 bottles, i have to get a W, a I, and a N.

Now, these 3 letters can come in 3 draws, in 3!, ie. 6 ways.

Each has a probability of 1/3.

So, the required probability is

So, the probability of winning the prize just after 3 bottles, is 0.22.

Question 2

A license plate contains 3 numerals. Even and odd digits are equally likely.

So, the chance of having an even digit on any randomly selected place in the license plate, is 1/2.

We have to find the probability that all 3 numerals are even.

Now, each numeral will be even with probability 1/2.

So, the required probability is

So, the probability of all 3 numerals being even is 1/8, ie. 0.125.

Question 3

A restaurant gives away a model car with each meal.

We are equally likely to get any of the 5 cars.

We have to find the probability that I will get two of the same cars, after two meals.

Now, after the first meal, I can get any 1 of the 5. Irrespective of this, I can get any 1 of the 5 cars, after the second meal.

So, the all possible cases is =5*5, ie. 25.

Now, if I am to get two of the same cars after both meals.

So, first we choose which car I am to get. That can be done in 5 ways.

Now, I can get that car both times, in only 1 way.

So, the number of favourable cases is 5*1, ie. 5.

So, the required probability is

So, the probability that i will get two of the same cars, after two meals, is 0.2.