Probability of Binomial Distribution

Bob is taking a 100 question test.  They have a 90 % probability of getting any one question correct.  WHICH IS THE CORRECT FORMULA TO FIND OUT THE PROBABILITY that they will answer EXACTLY 70  questions correctly?

• ₁₀₀C₇₀   ( 0.18  )³⁰ ( 0.90  )⁷⁰
  

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁶⁰

• ₁₀₀C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

• ₉₉C₇₀   ( 0.10  )³⁰ ( 0.90  )⁷⁰

Is this binomial experiment? Shuffle a deck of 52 cards. Turn over the top card. Put the card back in the deck, shuffle again. Repeat the process 50 times. Let X = the number of aces you observe.

• Yes

• No, the trials are not independent.

• No, there are more than 2 outcomes

An algebra 2 test has 6 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 6 questions, what is the probability that you get exactly 3 questions correct? (You need to figure out the p value first. It is not given to you.)

• 0.962

• 0.132

• 0.831

• 0.250

A test consists of 10 multiple choice questions with five choices for each question.  As an experiment, you GUESS on each and every answer without even reading the questions. 
What is the probability of getting exactly 6 questions correct on this test?

• 0.6%

• 0.00001%

• 0.0064%

• 0.0002%

A test has 8 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 8 questions, what is the probability that you get at least 3 questions correct?

• 0.886

• 0.332

• 0.678

• 0.208

The random variable, X has the binomial distribution X~B(9,0.25), find P(X=4)

• 0.1657

• 0.1168

• 0.2336

• 0.3504

The random variable Y has binomial distribution Y~B(10,0.4). Find P(3<Y<6)

• 0.6665

• 0.7779

• 0.4515

• 0.2508

The random variable T has binomial distribution T~(40,0.5). Find P(T≤12)

• 0.0032

• 0.0051

• 0.9968

• 0.0083

A ball manufacturer claims that only 15% of his balls are defective. If Ali has 6 of these balls to play with at a ball game, find the probability at most 4 balls will be defective.

• 0.9941

• 0.0059

• 0.9996

• 0.9527

The probability Ali wins a chess game is 0.4. Given that he plays only 5 games a week, find the probability that in any week he wins at least 2 games.

• 0.6630

• 0.3370

• 0.9222

• 0.3456