Practice: two-stage experiments
Practice: two-stage experiments
A blue die and a red die are thrown.
Mark the cells of the event “the sum is 9”.
What is the probability that the sum is 9?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What is the probability that the sum is not 9?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A blue die and a red die are thrown.
Mark the cells of the event “the blue die shows a larger number than the red one”.
What is the event’s probability?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Without marking cells: what is the probability that both dice show the same number?
And that the red die shows a larger number than the blue one?
Explain.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A coin is tossed and a die is thrown.
Mark the cells of the event “tails, and a prime number on the die”.
What is the event’s probability?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A bag holds 2 red marbles and 3 blue ones.
A marble is drawn, put back in the bag, and another marble is drawn.
Write the probabilities in the tree, and mark the paths of the event “the two marbles are different colours”.
What is the probability that the two marbles are different colours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
The same bag holds 2 red marbles and 3 blue ones.
This time a marble is drawn, not put back, and another marble is drawn.
Write the probabilities in the tree, and mark the paths of the event “the two marbles are different colours”.
What is the probability that the two marbles are different colours?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Compare with question 4: when is the probability of two different colours larger – with putting back or without?
Explain by what is left in the bag after the first draw.
A third of a spinner is red, and two thirds of it are blue.
The arrow is spun twice.
Write each rectangle’s area, and mark the rectangles of the event “red at least once”.
Find the event’s probability with the complement.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A basketball player scores a free throw with probability 0.7.
She throws twice, and the second throw does not depend on the first.
Write each rectangle’s area, and mark the rectangles of the event “she scores exactly once”.
What is the probability that she scores exactly once?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What is the probability that she scores at least once?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A blue die and a red die are thrown.
Mark the cells where neither die shows a 6.
Find the probability that at least one die shows a 6.
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
A club has 9 children: 4 boys and 5 girls.
Two of them are drawn to present the club at a ceremony.
Write the probabilities in the tree, and mark the paths of the event “a boy and a girl”.
What is the probability that a boy and a girl are drawn?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
What is the probability that two girls are drawn?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Dana and Yoav throw two dice.
Dana wins when the difference between the numbers is 0 or 1.
Yoav wins in every other case.
Write the difference in each cell (the larger number less the smaller), and mark the cells where Dana wins.
What is the probability that Dana wins?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Do both have the same chance of winning?
Explain.
A bag holds 3 red marbles and 2 blue ones.
A marble is drawn, not put back, and another marble is drawn.
Write each rectangle’s area, and mark the rectangles of the event “the second marble is red”.
What is the probability that the second marble is red?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
Compare with the probability that the first marble is red.
What do you find?
A bag holds one red marble and one blue marble.
A marble is drawn, and then another one.
What is the probability that both marbles are the same colour, if the first marble is put back?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
And what is this probability without putting back?
What kind of event is it?
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – check and a new line · * – times · ^ – power, ↓ – end of the power
/ – fraction bar · Tab or the arrows – between numerator and denominator, then a note above or below · Enter – a new line · * – times · ^ – power, ↓ – end of the power