9514 1404 393
Answer:
29) 1/5
30) independent; 64/225 ≈ 0.284
Explanation:
In general, a "spinner" is considered to be a (mathematically ideal) device that returns one of the values with which it is marked, with a probability according to the area of the sector in which the mark resides. Usually, sectors are presumed to have equal areas. The result of one spin is generally considered to be independent of the result from any other spin. In the real world, an operator familiar with a given spinner can often ensure that the results do not have equal probability and are not independent. We ignore that possibility in math problems.
__
29) Of the numbers 1 to 15, there are three numbers less than 4. The probability of spinning one of them is 3/15 = 1/5.
__
30a) We have defined our spinner so that the events are independent. (See above.)
30b) In the set of numbers 1 to 15, 8 are odd and 7 are even. The probability of getting an odd number on any spin is 8/15. Because the results of successive spins are independent, the probability of any given sequence is the product of the probabilities of the numbers in that sequence.
P(2 odd) = P(odd)×P(odd) = (8/15)(8/15) = 64/225 ≈ 0.284