Question

3) The chance that a salmon jumps up the waterfall to upstream successfully 35%. We have a group of 9 salmon. a) What is the chance that none of them jump up successfully? b) What is the chance that all of them reach up-stream? c) What is the chance that at least 2 of them reach up-stream? d) What is the chance that at most 1 of them reach up-stream? e) Is "at least 1" complement of event "at most 1"?

Answer 1

Let , X be the number of salmon jump up successfully.

p = probability of success = 35% = 0.35

Sample size = n = 9

X follows Binomial distribution with n = 9 and p = 0.35

a)

we have to find P( x = 0 )

Using Excel function , "=BINOMDIST(x, n , p, 0 ) "

P( x = 0 ) = BINOMDIST(0,9, 0.35, 0 ) = 0.02071

The chance that all of them reach up-stream is 0.02071

b)

we have to find P( x = 9 )

Using Excel function , "=BINOMDIST(x, n , p, 0 ) "

P( x = 9 ) = BINOMDIST(9,9, 0.35, 0 ) = 7.88156E-05 = 0.00008

The chance that all of them reach up stream is 0.00008

c)

We have to find P( x $_{\geq}$ 2 )

P( x $_{\geq}$ 2 ) = 1 - P( x $_{\leq}$ 1 )

Using Excel function , "=BINOMDIST(x, n , p, 1 ) "

P( x $_{\leq}$ 1 ) = BINOMDIST(1, 9, 0.35, 1 ) =0.121085

So,  P( x $_{\geq}$ 2 ) = 1 - 0.121085 = 0.87891

The chance that at least 2 of them reach up stream is 0.87891

d)

We have to find P( x $_{\leq}$ 1 )

Using Excel function , "=BINOMDIST(x, n , p, 1 ) "

P( x $_{\leq}$ 1 ) = BINOMDIST(1, 9, 0.35, 1 ) =0.121085

The chance that at most 1 of them reach up stream is 0.121085

e)

The event " at least 1" is not complement of event " at most 1"

{ complement of event " at least 1" is " less than 1 " }