Question

A group of hens lays 68 eggs in a single day. On one particular day, there were 7 brown eggs and 61 white eggs. If four eggs are selected at random, without replacement, what is the probability that all four are brown?

Give your answer as a decimal or in standard scientific notation with at least 3 significant digits.

Use an asterisk "*" to represent multiplication; do not use the E notation that the calculator uses.

Answer 1

The probability of selecting a brown egg on the first draw is 7/68. Since we are selecting without replacement, the probability of selecting another brown egg on the second draw is 6/67. Similarly, the probability of selecting a third brown egg is 5/66, and the probability of selecting a fourth brown egg is 4/65. Therefore, the probability of selecting four brown eggs is:

(7/68) * (6/67) * (5/66) * (4/65) = 0.000414

Rounding to three significant digits, the answer is 0.000414 or 4.14*10^-4.