First slide

Random variable and probability distribution

Question

$Let C_{1} and C_{2} be two biased coins such that the probabilities of getting head in a single toss are \frac{2}{3}$
$and \frac{1}{3}, respectively. Suppose α is the number of heads that appear when C_{1} is tossed twice,$
$independently, and suppose β is the number of heads that appear when C_{2} is tossed twice,$
$independently, Then probability that the roots of the quadratic polynomial x^{2} - α x + β are real and equal is$

Difficult

A

$\frac{40}{81}$
B

$\frac{20}{81}$
C

$\frac{1}{2}$
D

$\frac{1}{4}$

Solution

$\begin{aligned} P (H) = \frac{2}{3} for C_{1} \\ P (H) = \frac{1}{3} for C_{2} \end{aligned}$

$f o r C_{1}$
$for C_{2}$
$\begin{array}{l} for real and equal roots \\ α^{2} = 4 β \\ (α, β) = (0, 0), (2, 1) \\ So, probability = \frac{1}{9} \times \frac{4}{9} + \frac{4}{9} \times \frac{4}{9} = \frac{20}{81} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App