A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is

The following are the two statements relating to the theory of probability. Indicate the statements being correct or incorrect.
Statement I The probability of the joint occurrence of independent events A and B is equal to the probability of event A multiplied by the probability of event B or vice-versa.
Statement II The probability of the joint occurrence of independent event A and dependent event B is equal to the probability of event A multiplied by the conditionalprobability of event B when event A has occurredor vice-versa.

A

Both statements are correct

B

Both statements are incorrect

C

Statement I is correct while Statement II is incorrect

D

Statement I is incorrect while Statement II is correct

The probability is 1/2 that a coin will turn up heads on any toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

A

1/8

B

1/2

C

7/8

D

None of these

A coin is tossed twice if the coin shows head it is tossed again but if it shows a tail then a die is tossed. If 8 possible outcomes are equally likely. Find the probability that the die shows a number greater than 4, if it is known that the first throw of the coin results in a tail

A

1\/3

B

2\/3

C

2\/5

D

4\/15

If a fair coin is tossed four times. What is the probability that two heads and two tails will result?

A

$$\frac{3}{8}$$

B

$$\frac{1}{2}$$

C

$$\frac{5}{8}$$

D

$$\frac{3}{4}$$

A fair coin is tossed n times. The probability that the difference between the number of heads and tails is (n - 3) is

A

$${2^{ - {\text{n}}}}$$

B

0

C

$${}^{\text{n}}{{\text{C}}_{{\text{n}} - 3}}\,{2^{ - {\text{n}}}}$$

D

$${2^{ - {\text{n}} + 3}}$$

A fair (unbiased) coin was tossed four times in succession and resulted in the following outcomes: i. Head, ii. Head, iii. Head, iv. Head. The probability of obtaining a 'Tail' when the coin is tossed again is

A

0

B

$$\frac{1}{2}$$

C

$$\frac{4}{5}$$

D

$$\frac{1}{5}$$

For each element in a set of size 2n, an unbiased coin is tossed. All the 2n coin tossed are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is

A

\

B

\

C

\

D

$$\frac{1}{2}$$

A fair coin is to be tossed 100 times with each toss resulting in a head or a tail. If H is the total number of heads and T is the total number of tails, which of the following events has the greats possibility?

A

H =50

B

T> 60

C

H 95

D

H>48 and T> 48

When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 3 times, what is the probability that it will land on the same side each time?

A

1/8

B

1/4

C

1/3

D

3/8

160 heads and 240 tails resulted from 400 tosses of a coin. Find a 95% confidence interval for the probability of a head. Does this appear to be a fair coin?

A

Cannot be said to be fair

B

Can be or cannot be said to be fair

C

Can be said to be fair

D

Yes with +1