Ví dụ 1.5. Một người đi mua hàng 3 lần. Xác suất lần đầu mua được hàng tốt là 0,7.
Nếu lần trước mua được hàng tốt thì khả năng lần tiếp theo mua được hàng tốt là 0,85;
còn nếu lần trước mua phải hàng xấu thì khả năng lần tiếp theo mua được hàng tốt là
0,6. Tính xác suất để:
a) Cả 3 lần người đó đều mua được hàng tốt.
b) Chỉ có lần thứ 2 người đó mua phải hàng xấu.

If the first time you can buy good products, the next time you can buy good products is 0.85; (I interpret this as, if you buy a good product, then the next time you buy a good product is 0.85).

And if the last time I bought a bad product, the next time I bought a good one is 0.6. Calculate the probability that:

a) All three times the person bought good goods.

P(Good on 1st shopping event AND Good on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Good on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st and 2nd shopping events yield Good) =

(0.7)(0.85)(0.85) =

0.50575

b) Only the second time that person buys a bad product.

P(Good on 1st shopping event AND Bad on 2nd shopping event AND Good on 3rd shopping event) =

P(Good on 1st shopping event) *P(Bad on 2nd shopping event | Good on 1st shopping event) * P(Good on 3rd shopping event | 1st is Good and 2nd is Bad shopping events) =

(0.7)(1-0.85)(1-0.6) =

(0.7)(0.15)(0.4) =

0.042