Hello kindly help me solve the one question please

2. (15 %) Consider the model below, where a political leader makes the choice about whether to appoint a competent minister or appoint an incompetent minister, and the minister makes the choice about whether to stage a coup or not stage a coup. The leader's pay-offs are on the left and the minister's pay-off are on the right. Under a competent minister, a coup succeeds with probability P, whereas a coup succeeds with probability 0.25 under an incompetent minister. In the case of a coup, the minister gains, apart from a baseline salary of 1, an additional pay-off of 4 if a coup succeed and -4 if the coup fails. The leader gains a payoff of 4 if there is no coup and a competent minister and a payoff of 2 if there is no coup and an incompetent minister. If there is a coup, the leader gets a payoff of 0 and -4 if the coup succeeds. What is the maximum level that P (the probability that the coup is successful with a competent minister) can be, if the leader will still choose to appoint a competent minister? Show calculations. Leader Appoint incompetent Appoint competent minister minister Competent minister Incompetent minister No not stage coup Stage coup Do not stage coup Stage coup Coup successful: P Coup unsuccessful P*-4+0, 1 + P*4-4*(1-P) 4,1 2, 1 0.25*-4+0, 1 + 0.25*4-4*0.75