Math Problems 10/12/26

Question 1

## Warning: package 'lubridate' was built under R version 4.5.2

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The bar graph shows the number of kilograms of oranges bought by five friends. How many kilograms of oranges did Ramiro, Tom, and Ursula buy altogether?

# install.packages("tidyverse")
library(tidyverse)
q1_data <- data.frame(Name = c("Ramiro","Sian","Tom","Ursula","Vikram"),
                 kg = c(2,6,8,6,12))
answer <- q1_data %>%
  filter(Name %in% c("Ramiro","Tom","Ursula")) %>%
  select(kg) %>%
  sum()
cat("Ramiro, Tom, and Ursula bought",answer,"kilograms of oranges altogether.","\n")

## Ramiro, Tom, and Ursula bought 16 kilograms of oranges altogether.

Question 2

What is the least common multiple of 18 and 24?

# install.packages("pracma")
library(pracma)

## 
## Attaching package: 'pracma'

## The following object is masked from 'package:purrr':
## 
##     cross

Lcm(a = 18,b = 24)

## [1] 72

Question 3

The diagram shows a spinner made of a piece of card in the shape of a regular heptagon, with a toothpick pushed through its center. The seven triangles are numbered from 1 to 7. Each time, the spinner is spun until it lands on one of the seven edges of the heptagon. The spinner is spun six times. Use a Monte Carlo simulation to calculate the probability of three or more fives.

spinner <- 1:7
counter <- 0
N <- 1e5
for (i in 1:N) {
  spins <- sample(x = spinner,size = 6,replace = T)
  if (sum(spins == 5) >= 3) {
    counter <- counter + 1
  }
}
probability <- counter / N
cat("The probability is:",probability,"\n")

## The probability is: 0.04301