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Triple XXX Restaurant, a historic and popular diner in West Lafayette, has determined that the chance a customer will order a soft drink is 0.90. The probability that a customer will order a hamburger is 0.60. The probability that a customer will order French fries is 0.50. The restaurant has also determined that if a customer orders a hamburger, the probability the customer will also order fries is 0.80. Determine the probability that the order will include a hamburger and fries.

Sagot :

Answer:   0.48

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Explanation:

Define the events

  • D = person orders a drink
  • H = person orders a hamburger
  • F = person orders fries

The given probabilities are

  • P(D) = 0.90
  • P(H) = 0.60
  • P(F) = 0.50
  • P(F given H) = 0.80

The notation "P(F given H)" refers to conditional probability. If we know the person ordered a burger, then it changes the P(F) from 0.50 to 0.80; hence the events H and F are dependent.

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We want to find the value of P(H and F), which is the same as P(F and H)

We can use the conditional probability formula

P(F given H) = P(F and H)/P(H)

P(H)*P(F given H) = P(F and H)

P(F and H) = P(H)*P(F given H)

P(F and H) = 0.60*0.80

P(F and H) = 0.48

There's a 48% chance someone orders a burger and fries.

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