This question dey use Bayesian inference wey go help us use some information wey dem give us to find wetin we no sabi yet.

What H_1, H_2, H_3, and E dey represent

• H_1: Hiker dey for Area A. We fit talk am say P(H_1) = 1/6.
• H_2: Hiker dey for Area B. P(H_2) = 1/3.
• H_3: Hiker dey for Area C. P(H_3) = 1/2.

These H_1, H_2, and H_3 be the different hypotheses wey we dey try decide from. Dem show where the hiker fit dey.

• E: Plane see the hiker. So, the event E na "Plane spot the hiker if he dey for that area". Dem also give us some chances for how plane go fit spot the hiker depending on where the hiker dey:

  • If hiker dey Area A, chance say plane go see am na 50% (P(E|H_1) = 1/2).
  • If hiker dey Area B, plane go see am 30% of the time (P(E|H_2) = 0.3).
  • If hiker dey Area C, plane go see am 20% of the time (P(E|H_3) = 0.2).

Steps Dem Take for Bayesian Inference

1. Prior Probabilities (I):

   • Dis one na di first guess wey we get about where the hiker fit dey based on wetin dem tell us before the search start. We know say:
     • P(H_1) = 1/6
     • P(H_2) = 1/3
     • P(H_3) = 1/2

2. New Evidence from Plane Search (II):

   • Plane go search to help us find the hiker. Based on where di hiker dey, the plane get different chance to spot am:
     • If hiker dey A, chance say plane go see am na 50%.
     • If hiker dey B, na 30%.
     • If hiker dey C, na 20%.

3. Update Posterior Probabilities (III):

   • After we get di information (whether plane see hiker or no), we fit now update our belief for where di hiker fit dey based on di new data.

Na im be di events (i, ii, iii) for Bayesian inference.

I fit run calculation for the posterior probabilities for you if you like. Any questions so far?

Follow-Up Questions:

1. How dem take calculate posterior probability for Area A?
2. Wetin go happen if plane no spot the hiker at all?
3. How probability wey dem give for Areas B and C go affect di rescue team decision?
4. If plane spot the hiker, how ground-based team go take know which area to start search?
5. Wetin go happen if all the probabilities for plane spotting hiker change?

Tip:

When you dey use Bayesian inference, always remember say you fit update your beliefs as you get new evidence!