Zadanie 2a
Find (i) q; (ii) p and r.
- Materiał graficzny
Combined-event diagrams and probabilities
Use tables, trees or Venn diagrams to reason about combined, conditional and independent events with or without replacement.
Tę umiejętność sprawdza 35 zadań wzorowanych na arkuszach IB z lat 2022–2026.
Zadania sprawdzające tę umiejętność: 35 Otwórz w wyszukiwarce z filtrami
Zadanie 6a
Show that P(A) = (17 − x)/20.
Zadanie 8b
Show that a trial produces a flagged record with probability 1/5.
Zadanie 8c
For type S, P(S<200)=0.30854 and P(200<S<224)=0.62465. Independently select one battery of each type. Find the probability that at least one lasts more than 224 minutes.
Zadanie 9e
One play costs 6 credits. At least seven red markers win 50 credits, at least seven blue markers win B credits (a positive integer), and at least seven gold markers win 15 credits. Otherwise the prize is zero. These prize events are mutually exclusive. Let X…
Zadanie 5b
Show that C and D are independent.
Zadanie 7b
Find the probability of scoring zero.
Zadanie 7e
A player wins a bonus if the total score in exactly five rounds is greater than 48. Find the probability of winning the bonus.
Zadanie 8d
Given 490 ≤ D ≤ 520, find the probability that at most 501 visitors join soldering.
Zadanie 8e
A visitor joins 3D printing with probability 0.68, independently of that visitor’s soldering decision. Find the probability of joining both.
Zadanie 5a
State the probability of no alert from (i) check A; (ii) check B.
Zadanie 5b
(i) Show that 16k2 − 40k + 9 = 0. (ii) The roots of this equation are 1/4 and 9/4. State the valid value of k and justify your choice.
Zadanie 3b
Find P(A′ ∣ B′).
Zadanie 3b
Find P(A′ ∣ B′).
Zadanie 7c
Given that a randomly selected R device is at least 48 months old, find the probability that it is at least 72 months old.
Zadanie 7c
Given that a randomly selected R device is at least 36 months old, find the probability that it is at least 60 months old.
Zadanie 4
Events A,B satisfy P(A)=0.45, P(A|B)=0.30 and P(A∪B)=0.66. Find P(B).
Zadanie 8a
Find (i) p; (ii) q.
Zadanie 8b
Three distinct audited shipments are chosen uniformly without replacement. Find the probability that all three are regular.
Zadanie 8c
(i) Use P(R|B)=2/5 to find x. (ii) State the probability that a uniformly chosen audited shipment is regular and used a bike.
Zadanie 9a
In terms of n, give the probability that (i) the first card is marked; (ii) the first two cards are marked.
Zadanie 9b
For n=20, show that the first two cards are both unmarked with probability 33/95.
Zadanie 9c
For n=20, find the probability that the first three cards are unmarked.
Zadanie 9d
For n=20, find the probability that at least one of the first three cards is marked.
Zadanie 9e
Find the smallest number k of games for which the expected total score exceeds 160.
Zadanie 3a
Find P(A∪B).
Zadanie 3b
Hence or otherwise find P(A′∩B′).
Zadanie 3a
Find P(A∪B).
Zadanie 3b
Hence or otherwise find P(A′∩B′).
Zadanie 4
Independent events A,B satisfy P(A)=2P(B) and P(A∪B)=0.72. Find P(B).
Zadanie 9c
After three cycles the recorded total is 2 units. Find the probability the batch passes.
Zadanie 6a
Find P(A∩B) if the events are independent.
Zadanie 6b
Find the smallest possible value of P(A∩B).
Zadanie 6c
Find the largest possible value of P(A∩B), with a justification.
Zadanie 9b
Four cycles are checked in order. Find the probability that only the fourth lasts longer than 48 minutes.