Probability (a) What is the probability of rolling a pair of dice and obtaining

Question

Probability

(a) What is the probability of rolling a pair of dice and obtaining a total score of 9 or more? (b) What is the probability of rolling a pair of dice and obtaining a total score of 7?

A card is drawn at random from a deck. (a) What is the probability that it is an ace or a king? (b) What is the probability that it is either a red card or a black card?

  A fair coin is flipped 9 times. What is the probability of getting exactly 6 heads?

  You flip a coin three times. (a) What is the probability of getting heads on only one of your flips? (b) What is the probability of getting heads on at least one flip?

A jar contains 10 blue marbles, 5 red marbles, 4 green marbles, and 1 yellow marble. Two marbles are chosen (without replacement). (a) What is the probability that one will be green and the other red? (b) What is the probability that one will be blue and the other yellow?

You roll a fair die five times, and you get a 6 each time. What is the probability that you get a 6 on the next roll?

An unfair coin has a probability of coming up heads of 0.65. The coin is flipped 50 times. What is the probability it will come up heads 25 or fewer times? (Give answer to at least 3 decimal places).

True/False: You are more likely to get a pattern of HTHHHTHTTH than HHHHHHHHTT when you flip a coin 10 times. Explain why the answer is True or False.

Explanation / Answer

As per chegg rules,Never put more than 4 questions.

a)P(9 or more)->(4,5),(5,5),(3,6),(6,3),(6,4),(5,5),(6,4),(5,6),(6,5),(6,6)->10 ways

Hence P(9 or more)=10/36=5/18

P(score=7)->(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)->6 ways

Hence P(Score=7)=6/36=1/6

b)P(Ace or king)->4+13-1=16 ways

Hence Prob=16/52=4/13

P(Red or Black)=1

c)n=9,

P(6 heads)=9C6*0.5^9=0.1641

d)n=3

P(heads=1)=3C1*0.5^3=0.375

P(At least once)=1-P(None)=1-0.5^3=0.875

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