Binomial Distribution

State two conditions for a situation to be modelled by a binomial distribution

• Independent trials and has fixed probabilities

• Dependent trials and has fixed probabilities

• Independent trials and has not fixed probabilities

• Dependent trials and has not fixed probabilities

A fair three-sided spinner has sectors labelled 1,2,3. The spinner is spun until a 3 is scored. The number of spins required to get a 3 is denoted by X. Is this Binomial Distribution question?

• Yes

• No

On any school day, there is a probability of 0.3 that Jim’s parent is picking him up quite late. Nine days are chosen at random. Find the probability that Jim’s parent is late on more than 7 days. 

• $X\sim B\left(9,0.7\right),\ \ P\left(X>7\right)$
  

• $X\sim B\left(9,0.3\right),\ \ P\left(X>7\right)$

• $X\sim B\left(9,0.3\right),\ \ P\left(X\ge7\right)$

• $X\sim B\left(9,0.7\right),\ \ P\left(X\ge7\right)$

Probability that at most 4  

•  $P\left(X>4\right)$  

•  $P\left(X\ge4\right)$  

•  $P\left(X<4\right)$  

•  $P\left(X\le4\right)$  

Biscuits are sold in packet of 10. There is a constant probability that any biscuit is broken, independently of other biscuits. the mean number of biscuits in packet has been found to be 2. find the probability of any biscuit is broken.

• 0.6

• 0.8

• 0.2

• 0.4

X∼B(6,0.9).

Find Probability that at least 2 ?

• $P\left(x\ge2\right)$ =P(3)+P(4)+P(5)+P(6)
  

• $P\left(x>2\right)$ =P(3)+P(4)+P(5)+P(6)
  

• $P\left(x\ge2\right)$ =1-P(0)-P(1)-P(2)

• $P\left(x\ge2\right)$ =1-P(0)-P(1)

 $X\sim B\left(5,0.2\right),\$  Find  $\ P\left(X=4\right)$  

• 0.0512

• 0.2048

• 0.4096

• 0.0064

On a certain road 20% of the vehicles are trucks, 16% are buses and the remainder are cars. A random sample of 11 vehicles is taken. Find the probability that fewer than 3 are buses.

• 0.747

• 0.748

• 0.749

• 0.746