Zadanie 2c
Show that membership of C and membership of D are not independent.
Conditional probability and independence tests
Apply conditional-probability formulae and determine whether events are independent using an explicit mathematical test.
Tę umiejętność sprawdza 31 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 31 Otwórz w wyszukiwarce z filtrami
Zadanie 6b
A and B are independent. Find all possible x.
Zadanie 6
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 6b
Find P(X = 12 ∣ X ≥ 9).
Zadanie 8c
Given that the record is flagged, find the probability that station A was selected.
Zadanie 8a
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 8b
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 5a
Find .
Zadanie 5b
Show that C and D are independent.
Zadanie 7c
Calculate P(X ≥ a ∣ X < 4a).
Zadanie 3b
Show that A and B are not independent.
Zadanie 3c
Find P(A ∣ B′).
Zadanie 4a
Find .
Zadanie 4b
Find P(A ∣ B′).
Zadanie 6b
Given E, find the probability that workflow A was used.
Zadanie 9a
Let p and q be the probabilities that the second token is amber or violet, respectively, conditional on a violet first selection. Find p,q.
Zadanie 9b
Show that the probability of two selections of the same colour is 10/21.
Zadanie 9c
Given that the two selections have the same colour, find the probability that both are amber.
Zadanie 9f
Restart with 4 amber and 2 violet tokens and continue the same replacement rule until the first violet selection. Given that the first two selections are amber, state the probability that the third is violet.
Zadanie 9g
Restart with 4 amber and 2 violet tokens and continue the same rule until the first violet selection. The probability that the first violet occurs on selection n is 20/189. Find n.
Zadanie 8d
Are R and B independent? Justify your answer.
Zadanie 9c
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 9c
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 4
Independent events A,B satisfy P(A)=2P(B) and P(A∪B)=0.72. Find P(B).
Zadanie 6a
Find x.
Zadanie 6b
Find P(A′|B′).
Zadanie 9c
A piece is selected from the combined output. (i) Find the probability its thickness is below 117 μm. (ii) Given that its thickness is below 117 μm, find the probability it came from line A.
Zadanie 9d
Line A is adjusted: its mean stays 120 μm but its standard deviation becomes σ>0. Line B and the output proportions are unchanged. The combined probability of thickness below 117 μm is now 0.18. Find σ.
Zadanie 9c
After three cycles the recorded total is 2 units. Find the probability the batch passes.
Zadanie 9d
Given at least one breach in those six days, find the probability of fewer than four breaches.
Zadanie 9c
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…