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Tree diagram for two spins of a fair five-sector spinner and the probability of at least one red

Tree diagram for two spins of a fair five-sector spinner and the probability of at least one red

4 marks

A fair spinner has five equal sectors. One sector is red and the other four are green. The spinner is spun twice, and on each spin the result is recorded as red or not red.

______
red
______
not red
______
red
______
______
not red
______
______
red
______
______
not red
______
Outcomes
  1. Write the probability on each branch of the tree diagram, and write the outcome of each path in the space at its end.
  2. Find the probability that the spinner lands on red at least once in the two spins.

[4]

Solution:

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Answer:(a) each red branch \(\dfrac15\), each not-red branch \(\dfrac45\); outcomes: red, red; red, not red; not red, red; not red, not red (b) \(\dfrac{9}{25}\)

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