Free Printable End of week 12 Statistics assessment

1.

This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads. For the coin, P(H) = $\frac{2}{3}$ and P(T) = $\frac{1}{3}$ where H is heads and T is tails.

Find P(tossing a Head on the coin AND a Red bead)

a)

$\frac{2}{3}$

b)

$\frac{5}{15}$

c)

$\frac{6}{36}$

d)

$\frac{5}{36}$

2.

A bag contains 3 blue balls and 7 red balls. David selects 2 balls without replacement and draws the following tree diagram.

Given that the first ball is red, find the value of 𝑥 that represents the probability that the second ball selected is red.

a)

$\frac{2}{3}$

b)

$\frac{3}{5}$

c)

$\frac{7}{10}$

d)

$\frac{1}{3}$

e)

$\frac{7}{9}$

3.

This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y) and five blue (B) beads. For the coin, P(H) = $\frac{2}{3}$ and P(T) = $\frac{1}{3}$ where H is heads and T is tails.

Find P(Blue bead).

a)

$\frac{15}{36}$

b)

$\frac{10}{36}$

c)

$\frac{6}{36}$

d)

$\frac{10}{12}$

4.

There are 12 sweets in a bag

7 are lemon and 5 are orange.

Two sweets are taken out at random without replacement.

Work out the probability that the two sweets are the same Flavor

a)

b)

c)

d)

5.

13 of the 20 students in Mr Davidson’s class are girls.

Two students are chosen at random.

Work out the probability of two girls

being selected.

(Write your answer as a fraction in the simplest form using the / symbol e.g. 1/2)

(a)

6.

Liam chooses a card from a standard deck of 52 playing cards. He records whether it is one of the 12 face cards, that is, king, queen, or jack, or just an ordinary number card. Then, without putting the card back in the deck, he chooses another one. Which tree diagram correctly represents these two successive events?

a)

b)

c)

d)

7.

A box contains ten balls numbered from 1 to 10. Liam chooses one ball at random, without replacing it, and notes whether the number is prime or nonprime. Liam then chooses a second ball, again noting whether the number is prime or nonprime.

Work out the missing probabilities 𝑥 and 𝑦 in the tree diagram below, giving your answers as fractions in their simplest form.

a)

𝑥= $\frac{5}{9}$ and 𝑦=

b)

𝑥= $\frac{4}{9}$ and 𝑦= $\frac{5}{9}$

c)

𝑥= $\frac{1}{3}$ and 𝑦= $\frac{2}{3}$

d)

𝑥= $\frac{2}{3}$ and 𝑦= $\frac{1}{3}$

8.

The tree diagram below shows events 𝑆 and 𝑇,where 𝑆 is the event of it being sunny and 𝑇 is the event of two students taking a trip to the beach.

Find the missing probabilities 𝑥 and 𝑦.

a)

𝑥=0.5 and 𝑦=0.8

b)

𝑥=0.6 and 𝑦=0.8

c)

𝑥=0.9 and 𝑦=0.6

d)

𝑥=0.6 and 𝑦=0.9

e)

𝑥=0.5 and 𝑦=0.9

9.

The tree diagram below shows events 𝑆 and 𝑇,where 𝑆 is the event of it being sunny and 𝑇 is the event of two students taking a trip to the beach.

What is the probability that the students take a trip to the beach? (Write your answer to 2 decimal places)

(a)

10.

13 of the 20 students in Mr Davidson’s class are girls.

Two students are chosen at random.

Work out the probability of two boys

being selected.

(Write your answer as a fraction in the simplest form using the / symbol e.g. 1/2)

(a)

11.

Given that there was no peanut butter, what is the probability that they were not brownies?

a)

0.88

b)

0.58

c)

0.05

d)

0.12

12.

P (brownies l no peanut butter)

a)

0.12

b)

0.88

c)

0.05

d)

0.58

13.

A bag contains 22 red balls and 15 black balls. Two balls are drawn at random with out replacement. Find the probability that the second ball is black given that the first ball is red. Give your answer to three decimal places.

(Hint: Use a tree diagram)

(a)

14.

It is a little-known fact that drugs have been used to enhance performance in sports since the original Olympic Games (776 to 393 BC). In fact, the origin of the word doping is thought to come from the Dutch word doop, which is a type of opium juice used by the ancient Greeks.

Drug testing has become standard practice. In 2003, after anonymous testing of almost 1,500 players, the Major League Baseball (MLB) announced that approximately 6%‎ of MLB players used performance-enhancing drugs. They got this result taking into account that there was a 5%‎ chance that those who had not taken drugs tested positive (false-positive effect) and a 10%‎ chance that those who had taken drugs tested negative (false-negative effect).

Find the probability that an MLB player chosen at random had not taken drugs and tested positive. Round your answer to three decimal places if necessary.

(Hint: use the tree diagram provided for you)

(a)

15.

It is a little-known fact that drugs have been used to enhance performance in sports since the original Olympic Games (776 to 393 BC). In fact, the origin of the word doping is thought to come from the Dutch word doop, which is a type of opium juice used by the ancient Greeks.

Drug testing has become standard practice. In 2003, after anonymous testing of almost 1,500 players, the Major League Baseball (MLB) announced that approximately 6%‎ of MLB players used performance-enhancing drugs. They got this result taking into account that there was a 5%‎ chance that those who had not taken drugs tested positive (false-positive effect) and a 10%‎ chance that those who had taken drugs tested negative (false-negative effect).

Find the probability that an MLB player chosen at random had taken drugs and tested positive. Round your answer to three decimal places if necessary.

(Hint: use the tree diagram provided for you)

(a)

16.

It is a little-known fact that drugs have been used to enhance performance in sports since the original Olympic Games (776 to 393 BC). In fact, the origin of the word doping is thought to come from the Dutch word doop, which is a type of opium juice used by the ancient Greeks.

Drug testing has become standard practice. In 2003, after anonymous testing of almost 1,500 players, the Major League Baseball (MLB) announced that approximately 6%‎ of MLB players used performance-enhancing drugs. They got this result taking into account that there was a 5%‎ chance that those who had not taken drugs tested positive (false-positive effect) and a 10%‎ chance that those who had taken drugs tested negative (false-negative effect).

Find the probability that an MLB player chosen at random had positive test results. Round your answer to three decimal places if necessary.

(Hint: use the tree diagram provided for you)

(a)

17.

Knowing that the dessert has peanut butter in it, what is the probability that it's brownies?

a)

1.58

b)

0.58

c)

0.02

d)

0.98

18.

In the final exams, 40% of the students failed chemistry, 25% failed physics, and 19% failed both chemistry and physics. What is the probability that a randomly selected student failed physics given that he failed chemistry?

Give your answer to 3 decimal places

(a)

19.

271 students voted for the types of music they wanted at the school dance. The results are shown in the Venn diagram.

Find the probability that a randomly selected student voted for rock and not jazz.

Write you answer as a fraction in its simplest form using the / symbol e.g. 13/17.

(a)

20.

A class contains 100 students; 70 of them like mathematics, 60 like physics, and 40 like both. If a student is chosen at random, using a Venn diagram, find the probability that they like physics but not mathematics.

Write your answer as a decimal (1 decimal place)

(a)

End of week 12 Statistics assessment

Total questions: 20

Worksheet time: 13mins

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