Question

A number is selected randomly from a container containing balls labeled 1-40. Find: P(greater than 26 | odd)

a) 7/40
b) 13/40
c) 26/40
d) 20/40 (or simplified as 1/2)

Answer 1

The conditional probability that a randomly selected number from balls labeled 1-40 is greater than 26 given that it is odd is 7/20 or 35%.

Step-by-step explanation:

The question is asking for the conditional probability P(greater than 26 | odd), meaning the probability that the number is greater than 26 given that it is an odd number. There are 40 balls, and because every alternate number is odd starting from 1, there are 20 odd numbers in total (1, 3, 5, ..., 39). To find the odds that are greater than 26, we list the odd numbers greater than 26: 27, 29, 31, 33, 35, 37, and 39. There are 7 such numbers. Therefore, the probability is the number of favorable outcomes (odd numbers greater than 26) divided by the total number of possible outcomes (all odd numbers), which is 7/20, simplifying to 0.35 or 35%.