Zadanie 1b
Under the same w=3, p=1/3 settings, a run is still active at charge 1 after tick 4. State the probability that it is again active at charge 1 after the next two ticks.
Conditional probability and independence tests
Apply conditional-probability formulae and determine whether events are independent using an explicit mathematical test.
Tę umiejętność sprawdza 25 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 25 Otwórz w wyszukiwarce z filtrami
Zadanie 4b
Find P(X = 12 ∣ X ≥ 9).
Zadanie 5b
A and B are independent. Find all possible x.
Zadanie 5
A process duration H is normally distributed with mean μ seconds and standard deviation σ seconds. It is known that P(H > 48) = 0.35 and P(H > 54 ∣ H > 48) = 0.40. Find μ and σ.
Zadanie 10a
For a randomly selected type-R battery find the probability that its duration is (i) below 224 minutes; (ii) between 224 and 242 minutes; (iii) between 224 and 242 minutes given it exceeds 224 minutes.
Zadanie 10b
There are 24 registrations. Find (i) the probability that at least 16 attend; (ii) given that at least 16 attend, the probability that more than three fail to attend.
Zadanie 4a
Find .
Zadanie 4b
Show that C and D are independent.
Zadanie 4b
Now assume that A and B are independent. Find P(A′ ∣ B).
Zadanie 11c
A cycle is classified as short when T ≤ 6. Given that a selected cycle is short, find the probability that it lasts no more than 5.5 minutes.
Zadanie 11a
A processes 40 images. (i) Find the probability of at most five errors. (ii) Given at most five errors, find the probability of exactly three.
Zadanie 2a
Find .
Zadanie 2b
Find P(A ∣ B′).
Zadanie 7b
Given E, find the probability that workflow A was used.
Zadanie 11d
A coating has already lasted more than 6 days. According to the model, what is the probability that it lasts at least 6.6 days?
Zadanie 2h
In the continuous model q(x) = x2 + 2Zx + 4, with Z normal of mean 0.5 and standard deviation 1.5, suppose the graph has two distinct x-intercepts and . Find the conditional probability that both intercepts are greater…
Zadanie 11f
Consider n≥4 trials with exactly three successes, placed in n numbered circular slots in trial order. (i) Give the number of placements in which all three success slots are consecutive around the circle. (ii) Find the greatest n for which the conditional…
Zadanie 10c
For 60 independent readings, find (i) the probability exactly 15 are slow; (ii) the probability exactly 15 are slow, given fewer than 24 are slow.
Zadanie 10c
For 60 independent readings, find (i) the probability exactly 15 are slow; (ii) the probability exactly 15 are slow, given fewer than 24 are slow.
Zadanie 3
Independent events A,B satisfy P(A)=2P(B) and P(A∪B)=0.72. Find P(B).
Zadanie 5a
Find x.
Zadanie 5b
Find P(A′|B′).
Zadanie 8
A sensor of type A gives normally distributed signal readings with mean 48 and standard deviation 4. A type-B sensor has mean 50 and standard deviation 3. Every reading is independent, including across the two sensors. Each sensor is tested four times and…
Zadanie 10c
After three cycles the recorded total is 2 units. Find the probability the batch passes.
Zadanie 10c
A large collection contains only cycles longer than 48 minutes. (i) Find the probability that a randomly chosen cycle from this collection lasts less than 62 minutes. (ii) Twelve cycles are independently selected from the collection. Find the probability that…