SOLUTION: A radio station has a contest in which contestants toll a regular 6-sided die. If he rolls a 1 or 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $10
Algebra.Com
Question 1152116: A radio station has a contest in which contestants toll a regular 6-sided die. If he rolls a 1 or 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything. What is the probability that out of the first 5 contestants exactly 2 win $100?
Answer by greenestamps(13198) (Show Source): You can put this solution on YOUR website!
P(win $100) = 2/6 = 1/3 [win $100 with either a 3 or a 4]
P(other outcome ("lose")) = 2/3
The "probability vector" for each roll is
[1/3 chance of "winning" (W); 2/3 chance of "losing" (L)]
The probability that exactly 2 out of 5 contestants win $100 is the coefficient of the "(W^2)(L^3)" term in the expansion of
Expand using the binomial theorem. The coefficient of the (W^2)(Y^3) term is
= 0.3292181 to 7 decimal places.
If you have a TI83 calculator, you can confirm that result with
2nd-VARS
binompdf(5,1/3,2) [5 trials; 1/3 probability of winning; 2 successes]
RELATED QUESTIONS
In a simple game, a six-sided die is rolled 4 times. If all four rolls result in either... (answered by solver91311)
bobby has a game where he uses a six sided die. Each side of the die has one of the... (answered by stanbon)
If Jackson rolls a fair 6-sided die 200 times, what is a reasonable prediction on how... (answered by ikleyn)
A person rolls a standard six-sided die 10 times. In how many ways can he get 6 fives, 3... (answered by sudhanshu_kmr)
Two balanced 4 sided-dice, each with faces labeled by 1, 2, 3 and4.
if Ali plays a game... (answered by solver91311)
Matt thinks that he has a special relationship with the number 2. In particular, Matt... (answered by math_tutor2020)
Matt thinks that he has a special relationship with the number 2. In particular, Matt... (answered by proyaop)
the fm radio stations with high signal strength in new orleans breaks down into the... (answered by checkley77)
A game is played as follows: A player places a bet. Then, she rolls a 20-sided die with... (answered by shlomitg,math_tutor2020)