Question

There are 4 rotten eggs in a lot containing 20 eggs. Find the probability of getting a rotten egg if 2 eggs are chosen at random

Answer 1

The probability getting both rotten egg if two eggs are chosen at random is 0.7894

Step-by-step explanation:

Total eggs : 20 eggs

rotten eggs : 4 eggs

not rotten eggs : 16 eggs

To find the probability of getting both rotten egg if 2 eggs are chosen at the random

probability that the first egg chosen be rotten = $\frac{4}{20}$

if one egg is  chosen then remaining

total eggs = 20-1 = 19 eggs

total rotten eggs left = 4-1 = 3 eggs

now ,

probability that the second egg chosen to be rotten = $\frac{3}{19}$

then

the probability that both the eggs chosen are rotten = (probability of 1st egg is rotten )× ( probability of second egg is rotten)

= $\frac{4}{20}\times \frac{3}{19}$

=  $\frac{1}{5}\times \frac{3}{19}$

= 0.7894.. (approx)

hence,

The probability of getting both rotten egg if two eggs are chosen at random is 0.7894

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