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?

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 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

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

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

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

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

Consider the following statements.
1. If a person looks at a coin which is in a bucket of water, the coin will appear to be closer than it really is.
2. If a person under water looks at a coin above the water surface, the coin will appear to be at a higher level than it really is.
Which of the above statements is/are correct?

A

Both 1 and 2

B

Only 1

C

Only 2

D

Neither 1 nor 2

A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads?

A

(1\/2)^11

B

(9)(1\/2)

C

(11C2)(1\/2)^9

D

(1\/2)

A fair coin is tossed 10 times. What is the probability that ONLY the first two tosses will yield heads?

A

$${\left( {\frac{1}{2}} \right)^2}$$

B

$${}^{10}{{\text{C}}_2}{\left( {\frac{1}{2}} \right)^2}$$

C

$${\left( {\frac{1}{2}} \right)^{10}}$$

D

$${}^{10}{{\text{C}}_2}{\left( {\frac{1}{2}} \right)^{10}}$$

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

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

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 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