Question

Dashboard I Khan Academ X+ yorg Probability of "at least one" success Go to lesso You might need:Calculator When Ryan is serving at a restaurant, there is a0.75 probability that each party will order drinks with their meal During one hour, Ryan served 6 parties Assuming that each party is equally likety to order drinks, what is the probability that at least one party will not order drinks? Round your answer to the nearest hundredth P(at least one without drinks) Show Calculator Stuck? Watch a video or use a hint. Report a problem

Answer 1

Given that, there is 75% probability that the order drinks with their meal.

=> 100 - 75 = 25% probability that the party will not order drinks.

sample size ( n ) = 6

We want to find, P(at least one without drinks)

Let X be a number of parties will not order drinks.

Here, X ~ Binomial( n = 6, p = 0.25)

Probability mass function of X is,

P(X = x) = ⁿC_x p^x (1-p)^n-x

Therefore, P(X >= 1)

P(X >= 1)

= 1 - P(X < 1)

=1 - P(X = 0)

= 1 - [ ⁶C₀ (0.25)⁰ * (1 - 0.25)^6-0 ]

= 1 - [ 1 * 1 * (0.75)⁶ ]

= 1 - 0.1780

= 0.8220

=> P(X >= 1) = 0.8220= 0.82

Therefore, P(at least one without drinks) = 0.82