Hi, I'm struggling with this question I'm not sure how the textbook gets to the answer. Would anyone be able to help?

Q: The Apache Orchard grows a very juicy apple called the Fuji apple. Fuji apples are picked and then sorted by diameter into three categories:

• small — diameter less than 60 mm

• jumbo — the largest 15% of the apples

• standard — all other apples.

f) Some apples are selected before sorting and are packed into bags of 6 to be sold at the front gate of the orchard. Determine the probability, correct to 4 decimal places, that one of these bags contains at least 2 jumbo apples.

The answer given is

Hey Gracey1415,

I believe the distribution they give i.e. Y~Bi(6,0.15) is correct as the number of apples (n) is 6 and the probability of having a jumbo apple (p) is 15%=0.15. However, the probability the textbook states is incorrect. As they ask for the probability that one of these bags contains

**at least 2** jumbo apples, this means that the probability is actually

**P(Y≥2)** and not P(Y≤2). From here, you can either use the binomial probability formula (on the QCAA formula sheet) or use the Bcd function on your calculator to figure the answer out. I entered it into my calculator (as I'm too lazy to algebraically work it out) and the answer was indeed 0.2235.

Hope this helps! If you have any other questions or want me to elaborate, feel free to reply back! Good luck!