Question

Find the probability that in 200 tosses of a fair die, we will obtain at most 30 fives.

Answer 1

Given:

200 tosses of a die

To find:

The probability of getting at most 30 5s

Solution:

By binomial distribution,

Probability of success = p

p = P ( 5 )

p = 1 / 6

q = 5 / 6  

n = 200  

By formula,

Mean = np

Substituting,

We get,

200 * 1 / 6

Mean = 33.33

Standard deviation = √ [ n ( p ( 1 - p )  ]

Substituting,

√ ( ( 200 ) ( 1 / 6 ) ( 5 / 6 ) )

Standard deviation = 5.270

P ( x <= 30)

Z formula,

Z = ( x - Mean ) / Standard deviation  

P ( Z <= ( 40 - 33.33 ) / 5.270

Hence, P ( x <=30 ) = 1.758