In a lottery, the top cash prize was $663 million, going to three lucky winners. Players pick four different numbers from 1 to 52 and one number from 1 to 42. A player wins a minimum award of $150 by correctly matching three numbers drawn from the white balls (1 through 52) and matching the number on the gold ball (1 through 42). What is the probability of winning the minimum award?

Aresearch study is studying the effects of a new drug for osteoporosis alzheimer's disease (ad) for women above the age of 65 years. a group of individuals with osteoporosis is randomized into two groups. one group is treated conventionally, and the second group is treated with the new medication. assessments are made at 3, 6, 12, 36, and 48 months. the conventionally treated group is assessed for ad using a serum blood test, and the treatment group is assessed for ad using a pet radiotracer that binds to beta-amyloid plaques. in comparing these 2 trial arms, the authors of the study may encounter which type of bias? a. selection bias on the risk of developing b. measurement bias c. confounding bias d. recall bias e. lead-time bias