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scoundrel [369]

3 years ago

7

80% of an airline's flights depart on-time and 20% do not. Of those that depart on-time, 95% arrive on-time. Of those that depar

t late, 10% arrive on-time. What is the chance of someone taking a flight that will arrive on-time?

1 answer:

Dmitry_Shevchenko [17]3 years ago

4 0

Answer:

0.78

Step-by-step explanation:

given that 80% of an airline's flights depart on-time and 20% do not.

Of those that depart on-time, 95% arrive on-time. Of those that depart late, 10% arrive on-time

Let A be the event that flight departs on time.

Now A and A' are mutually exclusive and exhaustive

Let B be the event the flight arrives on time

Using total probability calculation we have

the chance of someone taking a flight that will arrive on-time

= P(B)

= $P(A)+P(A'B)\\= 0.80(0.95) +0.20(0.10)\\= 0.76+0.02\\=0.78$

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From the first statement. They served 23 grande cups and 51 jumbo cups of the new coffee today, which equal a total of 36,846 grams.

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$23x+51y = 36846$ ---------(1)

From the second statement. They served 58 grande cups and 68 jumbo cups of the new coffee tomorrow, which equal a total of 59460 grams.

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Solve the equation 1 for x.

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$x=\frac{36846}{23}-\frac{51}{23}y$

$x=1602-\frac{51}{23}y$ ---------(3)

Substitute $x=1602-\frac{51}{23}y$ in equation 2.

$58(1602-\frac{51}{23}y)+68y=59460$

$92916-\frac{51\times 58}{23}y+68y=59460$

$-\frac{2958}{23}y+68y=59460-92916$

$\frac{-2958+1564}{23}y=-33456$

$\frac{-1394}{23}y=-33456$

Using cross multiplication.

$y=\frac{-23\times 33456}{-1394}$

$y = 55.99$

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Substitute y = 60 in equation 3.

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$x=1602-\frac{3060}{23}$

$x=1602-133.04$

$x = 1469$ grams

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