Are the outcomes in the following experiments equally likely?

  1. A citizen of California is chosen at random and his or her town of residence is recorded.

No. Most California residents live in a few big cities such as Los Angeles or San Francisco and they’re more likely to be chosen.

  1. Two drug pills and three placebos (sugar pills) are placed in a container and one pill is chosen at random and its type is recorded.

No. It’s more likely that we choose a placebo.

  1. A snowflake is chosen at random and its appearance is recorded.

Yes. Snowflakes are unique so each one is equally likely to appear.

  1. Two fair dice are tossed and the sum of the numbers appearing is recorded.

No. The least likely outcomes are 2 (both dice come up 1) and 12 (both dice come up 6). The most likely outcome is 7 (can be thrown in 6 ways).

  1. A bit string of length 3 is chosen at random and the sum of its digits is observed.

No. Bit strings with sum 0 (000) and 3 (111) are not as likely as e.g. a bit string with sum 1 (there are 3 such strings).