Question

you roll three six sided dice. what is the probability that exactly two of the dice are odd?

Answer 1

Answer:

3C2 * (.5)^2 * (.5)^1

.375

Step-by-step explanation:

...

Answer 2

The probability that exactly two of the dice are odd is 3/8

What is probability?

"It is finding out the possibilities of the occurrence of an event."

Formula to find the probability of an event:

"P(A) = n(A) / n(S)

where, n(A) is the number of favorable outcomes of an event A

n(S) is the total number of outcomes for an experiment"

What is Binomial theorem of probability?

$P=~ ^nC_r\times p^r \times q^{n-r}$

where, p is the probability of success and q is the probability of failure

For given example,

We roll three six sided dice.

We need to find the probability that exactly two of the dice are odd

the probability of success i. e. dice is odd would be,

⇒ p = 3/6

⇒ p = 1/2

So, the probability of failure would be,

⇒ q = 1 - p

⇒ q = 1 - 1/2

⇒ q = 1/2

Also, n = 3 and r = 2

Using Binomial distribution the required probability would be,

$\Rightarrow P=~ ^nC_r\times p^r \times q^{n-r}\\\\\Rightarrow P=~ ^3C_2\times (\frac{1}{2} )^2 \times (\frac{1}{2} )^{3-2}\\\\\Rightarrow P =\frac{3!}{3!(3-2)!}\times \frac{1}{4} \times \frac{1}{2}\\\\ \Rightarrow \bold{P=\frac{3}{8}}$

Therefore, the probability that exactly two of the dice are odd is 3/8

Learn more about the probability here:

brainly.com/question/11234923

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