Answer to Question #210137 in Electrical Engineering for Bahawal Tahir

Question

Question2

a).A balanced coin is tossed three times. Calculate the probability that exactly two of the three tosses result in heads.

b). A coin is tossed and a single 6-sided die is rolled. Find the probability of getting a head on the coin anda 4 on the die?

c). Prove that the following events are independent or dependents

i) Tossing a pair of fair dice and two events A & B are defined as Sum equal to 3 and 6 respectively

ii) Toss a pair of fair dice with defining two events A and B as both red and green die show 2

iii) Toss a fair coin twice with defining two events A and Bas A: head on second toss

and B: head on first toss

d). Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then

one card is drawn randomly. If it is known that the number on the drawn card is

more than 3, what is the probability that it is an even number?

Answer 1

a) H represents a head while T represents a tail

$3$ $Heads$

$HHH$

$2$ $Heads$

$HHT$

$HTH$

$THH$

$1$ $Head$

$HTT$

$THT$

$TTH$

$Head$

$TTT$

$\frac3{1+3+3+1}=\frac{3}8$

b) $P(head)=\frac{1}2$

$P(4)=\frac{1}6$

$P(head \space and \space 4)=\frac{1}2*\frac{1}6=\frac{1}{12}$

c)i) Tossing a pair of fair dice is an example of an independent event . When tossing a dice , the probability of getting any number does not change no matter how many times you toss the dice.

ii) Toss a pair of fair dice with defining two events is independent because the outcome of A will not be affected by the outcome of B.

iii) tossing a fair coin twice with defining two events A and B is independent since the probability of B is the same whether event A occurs or not.

d) Total numbers more than $3=4,5,6,.....,10=7$

Even numbers more than $3= 4,6,8,10=4$

Probability $= \frac{4}7$