# Exam-Style Questions on Binomial Distribution

## Problems on Binomial Distribution adapted from questions set in previous Mathematics exams.

### 1.

IB Standard

Mr Willis goes to school (he's a Maths teacher) five times each week during term time. On any given day, the probability that he goes on an orange bus is $$\frac13$$.

(a) Write down the expected number of times that Mr Willis goes to work at his school on an orange bus in one week.

In one week, find the probability that he goes to work on an orange bus

(b) on exactly three days;

(c) on at least two days.

### 2.

IB Standard

A small digital storage manufacturer makes novelty USB drives which are given away at conferences. The probability that a drive is defective is 0.03. The factory tests a random sample of 200 drives.

(a) Find the mean number of defective drives in the sample.

(b) Find the probability that there are exactly ten defective drives in the sample.

(c) Find the probability that there is at least one defective drive in the sample.

### 3.

IB Analysis and Approaches

The probability of winning a gold coin in a game of chance is 0.6. The game is played six times. Find the probability of winning:

(a) at least two gold coins;

(b) a fourth gold coin on the sixth game.

### 4.

IB Applications and Interpretation

Bostock and Chandler play one game of Ultimate Noughts and Crosses online each day they are in quarantine.

The probability that Bostock wins a game is three times the probability that Chandler wins a game. It is not possible to have a draw.

(a) Find the probability that on any given day Bostock will win the game.

The quarantine lasts for 30 days.

(b) Find the probability the Bostock will win 20 times.

(c) Find the probability Chandler will win at most 9 times.

### 5.

IB Standard

At the south end of Playfair Amusement park are two games of chance, Beat The Goalie and Basketball Bounce.

For the Goalie game, the probability of winning is 0.1. If someone plays this game nine times:

(a) Find the probability that they win exactly three times.

For the Basketball game, the probability of winning is $$x$$. If someone plays it nine times.

(b) Write down an expression, in terms of $$x$$, for the probability of winning exactly three games.

(c) Hence, find the values of $$x$$ such that the probability of winning exactly three games is 0.2.

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