Respuesta :

The probability of rolling a die 10 times and obtaining odd digit 8 or less of the rolls is 529/512 = 1.033

Let us call, getting an odd no. on a roll of die, Success.

The, clearly, the probability p of Success is 3/6 = 1/2.

Hence, q = 1 −p = 1/2

If, X = x denotes the no. of success in n trials, then, X is a

Binomial Random Variable, with parameters

n = 10, and, p = 1/2.

Binomial Random Variable:

This is a specific type of discrete random variable. A binomial random variable counts how often a particular event occurs in a fixed number of tries or trials. For a variable to be a binomial random variable, ALL of the following conditions must be met:

  1. There are a fixed number of trials (a fixed sample size).
  2. On each trial, the event of interest either occurs or does not.
  3. The probability of occurrence (or not) is the same on each trial.
  4. Trials are independent of one another.

Then, the Probability of x success out of n trials, i.e.,

P (X = x), is,

P (X = x) = p(x) =ⁿCₓ pˣ , qⁿ⁻ˣ, x = 0,1,2, ........, n

In our case,

P (X = x) = ¹⁰Cₓ (1/2)ˣ (1/2)¹⁰⁻ˣ ,x = 0,1,2,..., 10, i.e.,

P (X = x) = p(x) = ¹⁰Cₓ (1/2)¹⁰ = ¹⁰Cₓ /1024, x = 0, 1, ..., 10.

Hence,

The Required Probability = P( X< 8),

⇒ P (X = 0)+ P( X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) +P(X = 6) +  P(X= 7) +  P(X =8)

⇒ 1/1024 ( 1 + 10 + 45 + 120 +210 + 252 + 210 + 120 +90)

⇒ 1/1024 ×1058

⇒ 529 / 512

⇒ 1.033

Learn more about Probability:

https://brainly.com/question/9793303

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