Sajid is training for a long jump competition. He counts any jump over $6\,\text{m}$ as a success. On any given day, the chance that his first jump is a success is $0.2$. For each later jump, the probability of success is $0.3$ if the preceding jump was a success and $0.1$ otherwise. Sajid makes three jumps.
(a)[2]
Draw a tree diagram to represent this information, making sure every probability is included.
(b)[5]
Find the probability that Sajid has exactly one success, provided that he has at least one success.
(c)[3]
Find the probability that the first three jumps are successes and the final three are failures, or that the first three jumps are failures and the last three are successes.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The first and second jumps are displayed correctly, together with the outcomes and probabilities.” …