Question

When I visit a local cafe, there's an $80\%$ probability that I'll order a sandwich, and a $70\%$ probability that I'll order a soup. If there's a $5\%$ probability that I don't order the sandwich or soup, then what's the probability that I order both the sandwich and soup

Answer 1

There is 55% probability that I order both the sandwich and soup

Explanation:

P(sandwich) = 0.8

P(Soup) = 0.7

P(neither sandwich nor soup) = 0.05

P(sandwich or soup) = 1 - P(neither sandwich nor soup)

P(sandwich or soup) = 1 - 0.05 = 0.95

P(Sandwich & Soup) = x

P(Sandwich only) = 0.8 - x

P(Soup only) = 0.7 - x

P(sandwich or soup) = P(Sandwich only) + P(Soup only) + P(Sandwich & Soup)

Note that P(neither sandwich nor soup) has already been used to get the P(sandwich or soup) and should not be included in the above formula. Don't make that mistake!

0.95 = 0.8 - x + 0.7 - x + x

0.95 = 1.50 - x

x = 1.50 - 0.95

x = 0.55

There is 55% probability that I order both the sandwich and soup