If one out of 10 coming ships is wrecked. Find the probability that out of five coming ships at least 4 reach safely.

Explanation

Probability of a ship to reach the shore safely `=(9)/(10)`
Probability that a ship get drowned `=(1 -(9)/(10)) =(1)/(10)`
Let X be the random variable showing the number of ships
reaching the shore safely .
`:. ` P(at least 4 reaching safely)
=P(4 reaching safely or 5 reaching safely )
=P(4 reaching safely )+ P(5 reaching safely)
`=P(X=4)+P(x=5)`
`=.^(5)C_(4).((9)/(10))^(4)+((9)/(10))^((5-4)) +.^(5)C_(4).((9)/(10))^(5).((1)/(10))^(0)`
`=(1)/(2).((9)/(10))^(4)+((9)/(10))^(5) =((9)/(10))^(5)((1)/(2)+(9)/(10))=(7)/(5).((9)/(10))^(4)`
Let `A =(7)/(5).((9)/(10))^(4) =(7xx (9)^(4))/(5xx(10)^(4)) `
`rArr log A =lgo 7 + 4 xx log 9- log 5 - 4 xx log 10`
`=(0.8451 +4 xx 0.9542 - 0.6990-4)`
` =- 0.9371 = bar(1).9629`
`rArr A =" antilog " (bar(1).9629)=0.9181`
Hence the required probability is 0.9181