IB Mathematics Analysis and Approaches Topic SL 4.8—binomial Distribution Questionbank (SL/HL)

IB Mathematics Analysis and Approaches Topic SL 4.8—binomial Distribution Questionbank (SL/HL) | RevisionDojo

Practice IB Mathematics Analysis and Approaches (AA) Topic SL 4.8—binomial Distribution with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for SL 4.8—binomial Distribution and mirrors Paper 1, 2, 3 style where relevant.

Get instant solutions, detailed explanations, and build confidence with questions aligned to IB examiner expectations.

Paper

Level

Question 1

SLPaper 2

A mobile app has a feature that successfully loads with probability $0.85$ each time it is accessed. A user accesses the feature $8$ times in a session. Let $Y$ be the number of times the feature successfully loads.

Find the probability that the feature successfully loads exactly $6$ times.

[3]

Find the probability that the feature successfully loads at least $7$ times.

[3]

Question 2

SLPaper 2

A charity raffle sells tickets. Each ticket has a $0.05$ probability of winning a prize. A group of $25$ tickets is purchased and let $W$ be the number of winning tickets. If at least $3$ tickets win, the group qualifies for a bonus draw, where each of these winning tickets has a $0.1$ probability of winning an additional prize.

Find the probability that the group qualifies for the bonus draw.

[3]

Find the expected number and variance of winning tickets in the original raffle.

[4]

Given that the group qualifies for the bonus draw, find the probability that exactly 4 tickets win in the original raffle. Include a probability distribution graph to illustrate the conditional probability.

[4]

In the bonus draw, let $V$ represent the number of additional prizes won. Find the expected number of additional prizes won, given that the group qualifies for the bonus draw.

[4]

The charity wants the probability of qualifying for the bonus draw to be at least $0.8$ by adjusting the number of tickets purchased, $n$ . Let $W$ now denote the number of winning tickets when $n$ tickets are purchased. Find the smallest value of $n$ .

[5]

Question 3

HLPaper 1

A discrete random variable $X$ represents the number of successful attempts in a sequence of 5 independent trials, each with a success probability of 0.3. The probability distribution of $X$ follows a binomial distribution.

Write down the probability mass function of $X$ .

[2]

Calculate the expected value $E (X)$ .

[2]

Find the variance $Var (X)$ .

[2]

Question 4

SL & HLPaper 2

Two fair 4-sided dice are rolled. Each die has faces numbered from 1 to 4.

List the sample space of all the outcomes of the two dice along with their sums.

[2]

Find the probability that the sum of the numbers on the two dice is greater than or equal to 6.

[2]

Find the probability that the sum of the numbers on the two dice is smaller than 6 through a different approach than the previous part.

[2]

Question 5

SLPaper 2

The random variable $Y$ has a binomial distribution with parameters $m$ and $q$ . It is given that $E (Y) = 4.8$ .

Find the least possible value of $m$ .

[2]

Given that $P (Y \leq 1) = 0.02611$ correct to $4$ significant figures, determine the value of $m$ and the value of $q$ .

[5]

IB Mathematics Analysis and Approaches SL 4.8—binomial Distribution Questionbank

Unlock all 26 questions with a free account

IB Mathematics Analysis and Approaches SL 4.8—binomial Distribution Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.8—binomial Distribution Questionbank

Unlock all 26 questions with a free account