An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years. Profit % 1 5 10 15 20 30 40 45 50 Probability 0 . 05 0 . 10 0 . 50 0 . 20 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 Calculate the expected profit on an investment of $ 50000 .

Given that, An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years. Profit % 1 5 10 15 20 30 40 45 50 Probability 0 . 05 0 . 10 0 . 50 0 . 20 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 Expected profit = ∑ i = 1 n x i p i = 1 × 0 . 05 + 5 × 0 . 10 + 15 × 0 . 2 + 20 × 0 . 05 + 30 × 0 . 04 + 40 × 0 . 03 + 45 × 0 . 02 + 50 × 0 . 01 + 10 × 0 . 50 = 13 . 35 % ∴ Expected profit on investment $ 50000 = 50000 × 13 . 35 100 = $ 6675 ∴ Expected profit = 13 . 35 % × 50 , 000 = $ 6675

An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years. Profit % 1 5 10 15 20 30 40 45 50 Probability 0 . 05 0 . 10 0 . 50 0 . 20 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 A woman considers investing $ 50000 with the company, but decides that her money is likely to earn more when invested over the same period in a savings account that pays r % compound interest per annum. Calculate, correct to 2 decimal places, the least possible value of r .

Given that, An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of 3 years. Profit % 1 5 10 15 20 30 40 45 50 Probability 0 . 05 0 . 10 0 . 50 0 . 20 0 . 05 0 . 04 0 . 03 0 . 02 0 . 01 Expected profit = ∑ i = 1 n x i p i = 1 × 0 . 05 + 5 × 0 . 10 + 15 × 0 . 2 + 20 × 0 . 05 + 30 × 0 . 04 + 40 × 0 . 03 + 45 × 0 . 02 + 50 × 0 . 01 + 10 × 0 . 50 = 13 . 35 % ∴ Expected profit on investment $ 50000 = 50000 × 13 . 35 100 = $ 6675 ∴ Expected profit = 13 . 35 % × 50 , 000 = $ 6675 In compound interest, Amount = P 1 + r 100 T p = Principle = $ 50 , 000 , T = 3 , r = ? A = 50 , 020 + 6675 = 56675 ⇒ 50000 × 1 + r 10 3 > 56675 ∴ r = 4 . 27

The faces of a biased die are numbered 1 , 2 , 3 , 4 , 5 and 6 . The random variable X is the score when the die is thrown. The probability distribution table for X is given. x 1 2 3 4 5 6 P X = x p p p p 0 . 2 0 . 2 The die is thrown 3 times. Find the probability that the score is at least 4 on at least 1 of the 3 throws.

Given that, The faces of a biased die are numbered 1 , 2 , 3 , 4 , 5 and 6 . The random variable X is the score when the die is thrown. The probability distribution table for X is given. x 1 2 3 4 5 6 P X = x p p p p 0 . 2 0 . 2 The die is thrown 3 times. We know that, ∑ i = 1 n p i x i = 1 ∴ P ( x = 1 ) + p ( x = 2 ) + P ( x = 3 ) + P ( x = 4 ) + p ( x = 5 ) + p ( x = 6 ) = 1 ∴ p + p + p + p + 0 . 2 + 0 . 2 = 1 ∴ 4 p + 0 . 4 = 1 ∴ 4 p = 0 . 6 ∴ P = 0 . 6 4 ⇒ p = 0 . 15 Now, n = 3 ⇒ P ( atleast 4 ) = P ( x = 4 ) + P ( x = 5 ) + p ( x = 6 ) = 0 . 15 + 0 . 2 + 0 . 2 = 0 . 55 ⇒ P ( No one ) = 1 - 0 . 55 = 0 . 45 ∴ P ( atleast 1 of 3 throws ) = 1 - P No one at 3 throws = 1 - C 3 3 × ( 0 . 45 ) 3 = 1 - ( 0 . 45 ) 3 ⇒ P ( No one ) = + 0 . 909

EASY

AS and A Level

IMPORTANT

Earn 100

The following table shows the probability distribution for the random variable $Y .$

$y$ $1$ $10$ $q$ $101$

$P (Y = y)$ $0.2$ $0.4$ $0.2$ $0.2$

Given that Var $(Y) = 1385.2,$ show that $q^{2} - 61 q + 624 = 0$ and solve this equation.

Important Questions on Probability Distributions

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 2

The following table shows the probability distribution for the random variable $Y .$

$y$	$1$	$10$	$q$	$101$
$P (Y = y)$	$0.2$	$0.4$	$0.2$	$0.2$

Find the greatest possible value of $E (Y)$ if the $Var (Y) = 1385.2$ .

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 3

An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of $3$ years.

Profit $\Rightarrow q^{2} - 619 + 624 = 0$	$1$	$5$	$10$	$15$	$20$	$30$	$40$	$45$	$50$
Probability	$0.05$	$0.10$	$0.50$	$0.20$	$0.05$	$0.04$	$0.03$	$0.02$	$0.01$

Calculate the expected profit on an investment of $$ 50000 .$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 3

An investment company has produced the following table, which shows the probabilities of various percentage profits on money invested over a period of $3$ years.

Profit $(%)$	$1$	$5$	$10$	$15$	$20$	$30$	$40$	$45$	$50$
Probability	$0.05$	$0.10$	$0.50$	$0.20$	$0.05$	$0.04$	$0.03$	$0.02$	$0.01$

A woman considers investing $$ 50000$ with the company, but decides that her money is likely to earn more when invested over the same period in a savings account that pays $r %$ compound interest per annum. Calculate, correct to $2$ decimal places, the least possible value of $r .$

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 4

A chef wishes to decorate each of four cupcakes with one randomly selected sweet. They choose the sweets at random from eight toffees, three chocolates and one jelly. Find the variance of the number of cupcakes that will be decorated with a chocolate sweet.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 5

The faces of a biased die are numbered $1, 2, 3, 4, 5$ and $6 .$ The random variable $X$ is the score when the die is thrown. The probability distribution table for $X$ is given.

$x$	$1$	$2$	$3$	$4$	$5$	$6$
$P (X = x)$	$p$	$p$	$p$	$p$	$0.2$	$0.2$

The die is thrown $3$ times. Find the probability that the score is at least $4$ on at least $1$ of the $3$ throws.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 6

A picnic basket contains five jars: one of marmalade, two of peanut butter and two of jam. A boy removes one jar at random from the basket and then his sister takes two jars, both selected at random.

Find the probability that the sister selects her jars from a basket that contains:

exactly one jar of jam

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 6

A picnic basket contains five jars: one of marmalade, two of peanut butter and two of jam. A boy removes one jar at random from the basket and then his sister takes two jars, both selected at random.

Find the probability that the sister selects her jars from a basket that contains:

exactly two jars of jam.

EASY

AS and A Level

IMPORTANT

Cambridge International AS & A Level Mathematics : Probability & Statistics 1 Course Book>Chapter 6 - Probability Distributions>END-OF-CHAPTER REVIEW EXERCISE 6>Q 6

A picnic basket contains five jars: one of marmalade, two of peanut butter and two of jam. A boy removes one jar at random from the basket and then his sister takes two jars, both selected at random.

Draw up the probability distribution table for $J,$ the number of jars of jam selected by the sister, and show that $E (J) = 0.8 .$

The following table shows the probability distribution for the random variable Y. y 1 10 q 101 P(Y=y) 0.2 0.4 0.2 0.2 Given that Var Y=1385.2, show that q2-61q+624=0 and solve this equation.

Important Questions on Probability Distributions

Learn and Prepare for any exam you want !

The following table shows the probability distribution for the random variable $Y .$

$y$ $1$ $10$ $q$ $101$

$P (Y = y)$ $0.2$ $0.4$ $0.2$ $0.2$

Given that Var $(Y) = 1385.2,$ show that $q^{2} - 61 q + 624 = 0$ and solve this equation.