Probability with replacement/sequential selection

Calculate probabilities when items are selected sequentially with or without replacement, often involving conditional probabilities or tree diagrams for multiple selections.

3 questions · Moderate -0.8

5.01a Permutations and combinations: evaluate probabilities
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OCR S1 2011 January Q4
7 marks Moderate -0.8
4 Jenny and Omar are each allowed two attempts at a high jump.
  1. The probability that Jenny will succeed on her first attempt is 0.6 . If she fails on her first attempt, the probability that she will succeed on her second attempt is 0.7 . Calculate the probability that Jenny will succeed.
  2. The probability that Omar will succeed on his first attempt is \(p\). If he fails on his first attempt, the probability that he will succeed on his second attempt is also \(p\). The probability that he succeeds is 0.51 . Find \(p\). \(530 \%\) of packets of Natural Crunch Crisps contain a free gift. Jan buys 5 packets each week.
OCR MEI S1 2009 January Q2
5 marks Moderate -0.8
2 Thomas has six tiles, each with a different letter of his name on it.
  1. Thomas arranges these letters in a random order. Find the probability that he arranges them in the correct order to spell his name.
  2. On another occasion, Thomas picks three of the six letters at random. Find the probability that he picks the letters T, O and M (in any order).
Edexcel S1 Q6
12 marks Moderate -0.8
6. The individual letters of the word STATISTICAL are written on 11 cards which are then shuffled. One card is selected at random. Find the probability that it is
  1. a vowel,
  2. a T, given that it is a consonant. The 11 cards are then shuffled again and the top three are turned over. Find the probability that
  3. all three of the cards have a T on them,
  4. at least two of the cards show a vowel.