Probability of combined events

The probabilities of Kam Seng passing in Science and Mathematics subjects are 0.78 and 0.56 respectively. Calculate the probability that at least one subject is passed.

• 0.9032

• 0.5336

• 0.4664

• 0.4368

A number is chosen at random from theset S = {x: x is an integer, $1\le x\le50$ }.
Calculate the probability of getting a factor number of 20 or a multiple of 8. 

•  $\frac{12}{50}$  

•  $\frac{13}{50}$  

•  $\frac{8}{25}$  

•  $\frac{6}{25}$  

Athletes M and N are involved in a 100 meter sprint race. If the probabilities of athletes M and N respectively passing the specified conditions are  $\frac{4}{5}\ and\ \frac{5}{6},$  find the probability that only one of the athletes successfully passes them. 

•  $\frac{2}{3}$  

•  $\frac{1}{6}$  

•  $\frac{3}{10}$  

•  $\frac{2}{15}$  

Mark has eight pencils and three of them are blue. 40% of the pencils Farhan owns are blue.  $\frac{1}{5}$  of the pencils owned by Suresh are blue. Mark, Farhan and Suresh each choose a pencil at random. 
Calculate the probability that at least two of them will choose a blue pencil. 

•  $\frac{3}{25}$  

•  $\frac{3}{100}$  

•  $\frac{43}{200}$  

•  $\frac{49}{200}$  

Event C and D are independent where P(C) = 0.96 and

P(C ∩ D) = 0.36.

Find P(D).

• 0.306

• 0.323

• 0.346

• 0.375

Five cards labelled with the letters "R, A, J, I, N" are put into a box. Two cards are taken out at random from the box one by one without replacement.

Which of the following is not the possible outcome for the event?

• (I, J)

• (J, J)

• (I, N)

• (R, A)

The diagram shows the cards in box M and box N. A card is chosen at random from each of the boxes.

Calculate the probability of getting a perfect square and a vowel.

• $\frac{1}{6}$

• $\frac{1}{4}$

• $\frac{3}{4}$

• $\frac{1}{2}$

The probability of a patient is infected with a virus is $\frac{1}{10}.$  

Two patients are selected at random to perform the screening at the same time. 

Calculate the probability that at least one of the patients selected is infected with the virus.

•  $\frac{1}{10}$  

•  $\frac{9}{50}$  

•  $\frac{19}{100}$  

•  $\frac{81}{100}$  

The cards labelled with the letters 

"K, E, B, O, L, E, H, J, A, D, I, A, N" are put in a container.  

Determine  $P\left(R\cup T\right).$  

•  $\frac{6}{13}$  

•  $\frac{7}{13}$  

•  $\frac{8}{13}$  

•  $\frac{9}{13}$  

Good Pizza Shop has sold 12 pieces of Chicago pizza, 8 pieces of Italian pizza and x pieces of New York pizza in one day. A piece of pizza is chosen at random, the probability of a piece of Chicago pizza or a piece of New York pizza being chosen is  $\frac{11}{15}$  .
Calculate the value of x. 

• 8

• 9

• 10

• 12