mechanism on the space shuttle has mechanical flaw malfunctioning 2.6​% of the time. Determine the actual odds against malfunction and odds in favor of malfunction. simplest form using whole numbers.

Answer 1

First let's distinguish between probability and odds.

We look at probability as the

number of successes

total number

and odds as

number of successes

number of failures

You can rewrite this as percentages as well as numbers.

If the mechanism fails 2.6% of the time, then the odds of failure is

2.6. = 2.6 = 0.02559

100-2.6 97.4

The odds against failure is the reciprocal of the above

97.4 = 37.46

2.6

Answer 2

2.6% = 0.026.

Malfunction odds: 0.026 / (1 - 0.026) = 0.026/0.974 = 26/974 = 13/487 and odds equal 13 to 487.

Not malfunction odds: 1 - 13/487 = 475/487 and odds equal 475:487