设Ai={第i个原件正常运行}i=1,2,3,4,5
B={系统正常运行}
P(B)=P(A3)P(B|A3)+P(A3逆)P(B|A3逆)
①P(B|A3)=P(A1∪A4)(A2∪A5)
=[P(A1∪A4)]²=(2p-p²)²
②P(B|A3逆)=P(A1A2∪A4A5)
=2p²-p的4次方
P(B)=P(A3)P(B|A3)+P(A3逆)P(B|A3逆)
=p(2p-p²)²+(1-p)(2p²-p4次方)
=2p²-2p³-5×p的4次方+2×p的5次方