NEW
New Website Launch
Experience the best way to solve previous year questions with mock tests (very detailed analysis), bookmark your favourite questions, practice etc...
1

### WB JEE 2008

Subjective

If an unbiased coin is tossed n times. Find the probability that head appears an odd number of times.

.

## Explanation

Let P = Probability of getting a head in a single trial = $${1 \over 2}$$.

Number of trials = n

and x = number of heads in n trials.

We have $$P(x = r) = {}^n{C_r}{p^r}{q^{n - r}}$$

$$= {}^n{C_r}{\left( {{1 \over 2}} \right)^r}{\left( {{1 \over 2}} \right)^{n - r}} = {}^n{C_r}{\left( {{1 \over 2}} \right)^n}$$

Now,

P(x = odd) = $$P(x = 1) + P(x = 3) + (x = 5) + ...$$

$$= {}^n{C_1}{\left( {{1 \over 2}} \right)^n} + {}^n{C_3}{\left( {{1 \over 2}} \right)^n} + {}^n{C_5}{\left( {{1 \over 2}} \right)^n} + ...$$

$$= ({}^n{C_1} + {}^n{C_3} + {}^n{C_5} + ...){\left( {{1 \over 2}} \right)^n}$$

$$= {2^{n - 1}} \times {1 \over {{2^n}}} = {1 \over 2}$$

$$\therefore$$ P(head appears an odd number of times) $$= {1 \over 2}$$.

### Joint Entrance Examination

JEE Main JEE Advanced WB JEE

### Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

NEET

Class 12