Question

Global Airlines operates two types of jet planes: jumbo and ordinary. On jumbo jets, 25% of the passengers are on business while on ordinary jets 30% of the passengers are on business. Of Global's air fleet, 40% of its capacity is provided on jumbo jets. (Hint: The 25% and 30% values are conditional probabilities stated as percentages.) What is the probability a randomly chosen business customer flying with Global is on a jumbo jet?

Answer 1

Answer:

Answer:

The  probability is  $P(J|B) = 0.36$

Step-by-step explanation:

B =business

J=jumbo

Or =ordinary

From the question we are told that  

     The proportion of the passenger on business in the ordinary jet  is $P(B| Or) = 0.25$

     The proportion of the passenger on business in the jumbo jet  is  $P(B|J) = 0.30$

     The  proportion of the passenger on jumbo jets is  $P(j) = 0.40$

      The   proportion of the passenger on ordinary jets is evaluated as

         $1 - P(J) = 1- 0.40 = 0.60$

According to  Bayer's theorem the probability a randomly chosen business customer flying with Global is on a jumbo jet is mathematically represented as

        $P(J|B) = \frac{P(J) * P(B|J)}{P(J ) * P(B|J) + P(Or ) * P(B|Or)}$

substituting values

         $P(J|B) = \frac{ 0.4 * 0.25}{0.4 * 0.25 + 0.6 * 0.3}$

         $P(J|B) = 0.36$

Step-by-step explanation: