Haley substituted the values of a, b, and c into the quadratic formula below. x = StartFraction negative (negative 10) plus or m
2 answers:
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Answer:
(a)
(i) The probability of getting at least one 3 when 9 fair dice are thrown is 0.8062.
(ii) The value of <em>n</em> is 12.
(b) The probability that Ronnie wins the game is 0.3572.
Step-by-step explanation:
(a)
(i)
The probability of getting a 3 on a single die roll is, .
It is provided that <em>n</em> = 9 fair dice are thrown together.
The outcomes of each die is independent of the others.
The random variable <em>X</em> can be defined as the number of die with outcome as 3.
The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 9 and .
Compute the probability of getting at least one 3 as follows:
Thus, the probability of getting at least one 3 when 9 fair dice are thrown is 0.8062.
(ii)
It is provided that:
P (X ≥ 1) > 0.90
Compute the value of <em>n</em> as follows:
Thus, the value of <em>n</em> is 12.
(b)
It is provided that the bag contains 5 green balls and 3 yellow balls.
Ronnie and Julie play a game in which they take turns to draw a ball from the bag at random without replacement.
The winner of the game is the first person to draw a yellow ball.
Also provided that Julie draws the first ball.
P (Ronnie Wins) = P (The 1st yellow ball is selected at an even draw)
= P (The 1st yellow ball is drawn at 2nd, 4th and 6th draw)
= P (1st yellow ball is drawn at 2nd)
+ P (1st yellow ball is drawn at 4th)
+ P (1st yellow ball is drawn at 6th)
Thus, the probability that Ronnie wins the game is 0.3572.