Question:

A pair of dice is thrown $200$ times. If getting a sum of $9$ is considered a success, then find the mean and the variance respectively of the number of successes.

Updated On: Dec 22, 2024
  • $\frac{400}{9}$, $\frac{1600}{81}$
  • $\frac{1600}{81}$, $\frac{400}{9}$
  • $\frac{1600}{81}$, $\frac{200}{9}$
  • $\frac{200}{9}$, $\frac{1600}{81}$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is D

Solution and Explanation

When a pair of dice is thrown, the sample space has $36$ equally likely outcomes. Outcomes favourable to sum of $9$ are $(5,\, 4)$, $(4,\, 5)$, $(6,\,3)$, $(3,\,6)$ only. So $p =$ probability (sum is $9$) $= \frac{4}{36} = \frac{1}{9}$, $\therefore q = 1-\frac{1}{9}= \frac{8}{9}$, $n = 200$ Hence, mean $= np= 200\left(\frac{1}{9}\right)= \frac{200}{9}$ and variance $= npq = 200\left(\frac{1}{9}\right)\left(\frac{8}{9}\right) = \frac{1600}{81}$
Was this answer helpful?
1
0

Top Questions on Conditional Probability

View More Questions

Concepts Used:

Semiconductors

Semiconductors are a crystalline solid materials, whose electrical conductivity lies between a conductor and an insulator. Semiconductors are mainly used in the manufacturing of electronic devices like capacitors, transistors, diodes, Integrated circuits, etc.

Properties of Semiconductor:

  1. Semiconductor acts like an insulator at Zero Kelvin. On increasing the temperature, it works as a conductor.
  2. Due to their exceptional electrical properties, semiconductors can be modified by doping to make semiconductor devices suitable for energy conversion, switches, and amplifiers.
  3. Lesser power losses.

Uses of Semiconductor:

  1. Semiconductors are widely used in manufacturing electronics devices like transistors, diodes, sensors, integrated circuits.
  2. Semiconductors are widely used in all electronic devices, like mobile phones, digital cameras, communication devices, trains, ATMs, etc.