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In a hurdle race a player has to cross 18 hurdles. The probability that will clear each hurdle is 6/9 , what is the probability that he will knock down fewer than 4 hurdles.

In a hurdle race a player has to cross 18 hurdles. The probability that will clear each hurdle is 6/9 , what is the probability that he will knock down fewer than 4 hurdles.

Grade:Upto college level

2 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Fewer than 4 means he will stop after 1 or 2 or 3, let p=2/3,q=1/3
=pqqqqqqqq(17q’s)+ppqqqqq(16q’s)+pppqqqqqqq(15q’s)
=18c0(2/3)18(1/3)0+18c1(2/3)17(1/3)+18c2(2/3)16(1/3)2+18c3(2/3)15(1/3)3
=0.1
Thanks and Regards
Shaik Aasif
askIITians faculty
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
Fewer than 4 means he will stop after 1 or 2 or 3, let p=2/3,q=1/3
=pppppppppppp.....(18p’s)+qppppppppp......(17p’s)+qqppppppppp......(16p’s)+qqqpppppp..........(15p’s)
=18c0(2/3)18(1/3)0+18c1(2/3)17(1/3)+18c2(2/3)16(1/3)2+18c3(2/3)15(1/3)3
=0.1
Thanks and Regards
Shaik Aasif
askIITians faculty

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