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09-18-2005, 11:48 PM
An angle is selected at random from the five angles and then replaced. A second selection is then made at random. (Thus, the same angle might be selected twice.) What is the probability that an acute angle is selected both times? The angles are as follows:
A = 50 degrees
B = 60 degrees
C = 90 degrees
D = 130 degrees
E = 40 degrees

the answer is 9/25
It appears that they take 3/5 and square it. Why?

soroban
09-19-2005, 12:05 AM
Hello, bonnielong!

An angle is selected at random from the five angles and then replaced.
A second selection is then made at random. (Thus, the same angle might be selected twice.)
What is the probability that an acute angle is selected both times?
The angles are as follows: A = 50°, B = 60°, C = 90°, D = 130°, E = 40°

The answer is 9/25
It appears that they take 3/5 and square it. Why?
Three of the five angles are acute.
The probability of selecting an acute angle is 3/5 each time, since there is replacement.

The probability that the first angle is acute is: 3/5
The probability that the second angle is acute is: 3/5

The probability that <u>both</u> are acute is: (3/5) x (3/5) .= .9/25