William works at West-Side Wanda\'s, a fast food franchise. He determines that t

Question

William works at West-Side Wanda's, a fast food franchise. He determines that the probability that customer orders French fries is .3, and the probability that a customer orders a soft drink is .55. The probability that they order a fries and a drink together is (.25).

a) Are they events "orders fries" and "orders soft drink" disjoint?

b) Are they events "orders fries" and "orders soft drink" independent?

c) Assuming that customers order independently of one another, what is the probability that two customers don't order fries?

d) What is the conditional probability that a customer orders a drink, given that they have ordered fries?

e) What is the conditional probability that a customer orders fries, given that they have ordered a drink?

Explanation / Answer

Here we have

P(orders fries and orders soft drinks)= 0.25

P(orders fries) = 0.3

P(orders soft drinks) = 0.55

(a)

No events "orders fries" and "orders soft drink" are not disjoint because P(orders fries and orders soft drinks) is not equal to zero.

(b)

P(orders fries)* P(orders soft drinks) = 0.3* 0.55 = 0.165

Since P(orders fries)*  P(orders soft drinks) is not equal to  P(orders fries and orders soft drinks) so events "orders fries" and "orders soft drink" are not independent.

(c)

The probability that customers don't order fries is

P(don't order fries) = 1 - P(order fries) = 1 - 0.3 =0.7

Since customers order independently of one another so  the probability that two customers don't order fries is

0.7 * 0.7 = 0.49

(d)

P( orders soft drink | order fries) =  P(orders fries and orders soft drinks) / P( orders fries) = 0.25 / 0.3 = 0.8333

(e)

P( orders fries | order soft drink) =  P(orders fries and orders soft drinks) / P( order soft drink) = 0.25 / 0.55 = 0.4545

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