Answer :
Answer:
the probability of getting exactly 2 fours is 0.16
Step-by-step explanation:
The probability of obtaining a number that is four = ¹/₆
The probability of obtaining a non 4 number = 1 - ¹/₆ = ⁵/₆
The number of ways 2 fours can be arrange in five numbers = ⁵C₂ = 10 ways
If the die is tossed five times, the probability of the events is calculated as;
P = 10 x (¹/₆)² x (⁵/₆)³
P = 10 x (¹/₃₆) x (¹²⁵/₂₁₆)
P = 10 x 0.02778 x 0.5787
P = 0.16
Therefore, the probability of getting exactly 2 fours is 0.16
The probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is [tex]0.1608[/tex].
Probability:
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are to happen, using it.
Let [tex]X[/tex] be the number of fours in [tex]5[/tex] coin tosses.
We have no. of tosses [tex]n=5[/tex].
Probability of a success i.e., getting four [tex](p)=\frac{1}{6}[/tex] and probability of not getting a four [tex](q)=\frac{5}{6}[/tex].
[tex]X[/tex] follows a binomial distribution. So,
[tex]P(X=x)=\binom{n}{x}p^{x}q^{n-x}[/tex]
[tex]\therefore[/tex] the probability of exactly [tex]2[/tex] four's in [tex]5[/tex] tosses is given by,
[tex]P(X=2)=\binom{5}{2}\left ( \frac{1}{6}^{2} \right )\left ( \frac{5}{6} \right )^{3}[/tex]
[tex]=0.1608[/tex]
Learn more about the topic of Probability: https://brainly.com/question/26959834