为普及抗疫知识、弘扬抗疫精神,某学校组织防疫知识挑战赛.每位选手挑战时,主持人用电脑出题的方式,从题库中随机出3道题,编号为
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,
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,
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,电脑依次出题,选手按规则作答,挑战规则如下:
①选手每答对一道题目得5分,每答错一道题目扣3分;
②选手若答对第
题,则继续作答第
题;选手若答错第
题,则失去第
题的答题机会,从第
题开始继续答题;直到3道题目出完,挑战结束;
③选手初始分为0分,若挑战结束后,累计得分不低于7分,则选手挑战成功,否则挑战失败.选手甲即将参与挑战,已知选手甲答对题库中任何一题的概率均为
,各次作答结果相互独立,且他不会主动放弃任何一次作答机会,求: