. formula is P(CRASH∣SHAKE)= P(SHAKE∣CRASH)×P(CRASH)+P(SHAKE∣¬CRASH)×P(¬CRASH) P(SHAKE∣CRASH)×P(CRASH)
options(scipen = 999) #not to show scientific number
P_CRASH <- 1/10000000 #st
P_SHAKE_given_CRASH <- 1
P_SHAKE_given_not_CRASH <- 1/100 # scariest flight you have been on, out of 100 similar trips
# Calculate P(not CRASH)
P_not_CRASH <- 1 - P_CRASH
# Calculate P(CRASH|SHAKE) using Bayes' theorem
P_CRASH_given_SHAKE <- P_SHAKE_given_CRASH * P_CRASH / (P_SHAKE_given_CRASH * P_CRASH + P_SHAKE_given_not_CRASH * P_not_CRASH)
# Print the result
print(P_CRASH_given_SHAKE)
## [1] 0.000009999901