Probability ?

[Paul Suszko]

The probability of a car with five worn tires will experience a blowout is 0.50. The probability of completing a trip with no more than one blowout is ?

 

[stapel]

What kind of car drives on five tires...? :shock:

Eliz.

 

[Paul Suszko]

One tire is the spare.

 

[pka]

Lets start with the four on car tires.
The probability of completing the trip on those is (0.5)<SUP>4</SUP>.

The probability at exactly one of those will fail 4(0.5)<SUP>4</SUP>.
Now we change to the spare and start out again.
The probability of completing the trip on those is (0.5)<SUP>4</SUP>.

Therefore, to complete the trip we must have no failures or exactly one.
(0.5)<SUP>4</SUP>+4(0.5)<SUP>4</SUP>(0.5)<SUP>4</SUP>=(0.5)<SUP>4</SUP>(1+4(0.5)<SUP>4</SUP>).

 

[Paul Suszko]

Thanks.