Question

(14.14) larry reads that 1 out of 6 eggs contains salmonella bacteria. so he never uses more than 5 eggs in cooking. if eggs do or don't contain salmonella independent of each other, find the probability (±±0.01) that at least 1 of larry's 5 eggs contains salmonella. rn note: please be sure you read the question as 'at least 1' and not instead just find the prob of exactly one. probability is about

Answer 1

we know that

The probability that "at least one" is the probability of exactly one, exactly 2, exactly 3, 4 and 5 contain salmonella.

The easiest way to solve this is to recognise that "at least one" is ALL 100% of the possibilities EXCEPT that none have salmonella.

If the probability that any one egg has 1/6 chance of salmonella

then

the probability that any one egg will not have salmonella = 5/6.

Therefore

for all 5 to not have salmonella

= (5/6)^5 = 3125 / 7776

= 0.401877 = 0.40 to 2 decimal places

REMEMBER this is the probability that NONE have salmonella

Therefore

the probability that at least one does = 1 - 0.40

= 0.60

the answer is

0.60 or 60%