Probability either variable is less than or equal to 4

Suppose X is a random Binom(10, .6) variable (10 flips of a coin with 60% chance of heads) and Y is a random Binom(10, .7) variable (10 flips of a coin with a 70% chance of heads), and they are independent.

What is the probability that either of the variables is less than or equal to 4?

This exercise is part of the course

Foundations of Probability in R

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Exercise instructions

Simulate 100,000 draws from each of X (10 coins, 60% chance of heads) and Y (10 coins, 70% chance of heads) binomial variables, saving them as X and Y respectively.
Use these simulations to estimate the probability that either X or Y is less than or equal to 4.
Use the pbinom() function to calculate the exact probability that X is less than or equal to 4, then the probability that Y is less than or equal to 4.
Combine these two exact probabilities to calculate the exact probability that either variable is less than or equal to 4.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Use rbinom to simulate 100,000 draws from each of X and Y
X <- 
Y <- 

# Estimate the probability either X or Y is <= to 4


# Use pbinom to calculate the probabilities separately
prob_X_less <- 
prob_Y_less <- 

# Combine these to calculate the exact probability either <= 4

Edit and Run Code