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Considers a sequence of tossing of a fair coin where the out comes of tosses are independent. The probability of getting the head for the third time in the fifth toss is

A

$$\frac{5}{{16}}$$

B

$$\frac{3}{{16}}$$

C

$$\frac{3}{5}$$

D

$$\frac{9}{{16}}$$

Correct Answer: $$\frac{3}{{16}}$$

A fair coin is thrown in the air four times. If the coin lands with the head up on the first three tosses, what is the probability that the coin will land with the head up on the fourth toss ?

A

3/4

B

1/2

C

1/8

D

1/16

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 fair coin is tossed three times in succession. If the first toss produces a head, then the probability of getting exactly two heads in three tosses is

A

$$\frac{1}{8}$$

B

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

C

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

D

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

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 coin is tossed twice. What is the probability of getting head on first toss and tail on second toss?

A

1/2

B

1/3

C

1/4

D

1

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

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

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

An unbiased coin is tossed five times. The outcome of each toss is either a head or a tail. The probability of getting at least one head is

A

$$\frac{1}{{32}}$$

B

$$\frac{{13}}{{32}}$$

C

$$\frac{{16}}{{32}}$$

D

$$\frac{{31}}{{32}}$$

A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is

A

$$\frac{1}{3}$$

B

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

C

$$\frac{2}{3}$$

D

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

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